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Simulation Modeling for

Staff Optimization of the

Toronto Emergency Medical

Services Call Centre

Gillian Chin & Jason Coke

A thesis submitted in partial fulfilment

of the requirements for the degree of

BACHELOR OF APPLIED SCIENCE

Supervisor: Professor M.W. Carter

Department of Mechanical and Industrial Engineering

University of Toronto

March 2008

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Abstract

The Toronto Emergency Medical Service (EMS) Call Centre is responsible for receiving 911

calls from the public and dispatching ambulances should they be required. The Call Centre faces

the issue of how many call takers to staff on the four 12-hour shifts. The purpose of this thesis is

to determine the effectiveness of the current staffing routine as well as calculating the optimal

number of call takers for any given hour of the week. There must be a balance between having

excess capacity for unexpected demand spikes, and keeping the number of call takers minimal to

save resources.

This analysis was performed by assessing approximately three years of historical data on calls to

EMS. A simulation model was built with Simul8 software to gauge the effects of different

combinations of call takers, across the standard shift patterns. Since historical demand for EMS

calls is rising, an increase in call volume was also simulated to determine if current EMS staffing

levels are suitable for the future. Finally, an Excel spreadsheet was built as a model to validate the

results found in Simul8.

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Acknowledgements

We would like to extend our gratitude to the following for their time, efforts and expertise in

supporting us for the duration of this thesis.

Professor Michael Carter

Dave Lyons, Manager of the Toronto EMS System Control Centre Design Project

Dan Cottom, Coordinator, Control Centre Design Project, Toronto EMS

Adrian, Data Analyst, Toronto EMS

Wallace Law, Indy 0T7+PEY and Visual8 Consultant

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Table of Contents

ACKNOWLEDGEMENTS ..............................................................................................................................I

TABLE OF CONTENTS ................................................................................................................................II

LIST OF FIGURES ...................................................................................................................................... V

LIST OF TABLES ....................................................................................................................................... VI

1.0 INTRODUCTION .................................................................................................................................. 1

1.1 PURPOSE ................................................................................................................................................. 1 1.2 BACKGROUND .......................................................................................................................................... 1 1.3 MOTIVATION ............................................................................................................................................ 2 1.4 OBJECTIVES .............................................................................................................................................. 3

2.0 LITERATURE REVIEW ........................................................................................................................... 5

2.1 THE USE OF SIMULATION FOR MODELING/ANALYSIS........................................................................................ 5 2.2 QUEUING THEORY AS A VIABLE METHODOLOGY OF DATA REPRESENTATION ......................................................... 7 2.3 SIMULATION AND QUEUING THEORY IN RELATION TO CALL CENTRES ................................................................... 8 2.4 SIMULATION AND QUEUING THEORY IN RELATION TO EMERGENCY SERVICES ...................................................... 10

3.0 METHODOLOGY ................................................................................................................................ 12

3.1 DESCRIPTION OF CALL RECEIVING SYSTEM .................................................................................................... 12 3.1.1 Description of General System for Call Receiving: ...................................................................... 12 3.1.2 Description of ACD Specific Call Receiving System ..................................................................... 14

3.2 DATA ANALYSIS ...................................................................................................................................... 15 3.2.1 Incoming Call Distributions/Inter-arrival Rates .......................................................................... 15 3.2.2 Call Durations ............................................................................................................................. 19 3.2.3 Call Duration Distribution ........................................................................................................... 20

3.3 ENTERING DATA INTO THE SIMULATION MODEL ............................................................................................ 22 3.3.1 Incoming Call Distributions/Inter-arrival Rates .......................................................................... 22 3.3.2 Call Duration Distribution ........................................................................................................... 22

4.0 THE SIMULATION MODEL ................................................................................................................. 23

4.1 DATA DEVELOPMENT: LEARNING THE SYSTEM .............................................................................................. 23 4.2 PHYSICAL STRUCTURE OF THE SIMULATION ................................................................................................... 24

4.2.1 Call Arrivals ................................................................................................................................. 24 4.2.2 Queue for Incoming Calls ........................................................................................................... 24 4.2.3 Call Stations ................................................................................................................................ 25

4.3 VISUAL LOGIC COMMANDS ....................................................................................................................... 25 4.3.1 Inter-Arrival Rate Parameter Reset ............................................................................................ 25 4.3.2 Call Durations ............................................................................................................................. 26 4.3.3 Pre-emptive Call Priorities .......................................................................................................... 26 4.3.4 Incorporating Shift Patterns ....................................................................................................... 27

5.0 THE EXCEL MODEL ............................................................................................................................ 30

5.1 RATIONALE FOR THE NEED OF AN EXCEL MODEL ............................................................................................ 30 5.2 METHODOLOGY FOR CONSTRUCTING THE EXCEL MODEL ................................................................................ 30

5.2.1 The Numerical Representation ................................................................................................... 31 5.2.2 The Graphical Representation .................................................................................................... 31

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5.3 FUNCTIONALITY ...................................................................................................................................... 32 5.3.1 Parameter Changes .................................................................................................................... 32

5.3.1.1 Desired Busy Rate ................................................................................................................................ 32 5.3.1.2 Probability............................................................................................................................................ 32 5.3.1.3 Total Call Volume ................................................................................................................................. 33

5.3.2 Two Methods of Adjusting Call Volume ..................................................................................... 33 5.3.2.1 Adjusting by Total Call Volume ............................................................................................................ 33 5.3.2.2 Adjusting Call Volume by Hour of the Week ........................................................................................ 33

6.0 ANALYSIS OF RESULTS ...................................................................................................................... 37

6.1 – ANALYSIS OVERVIEW ............................................................................................................................. 37 6.2 – VARIABLES .......................................................................................................................................... 38

6.2.1 – Time of Day.............................................................................................................................. 38 6.2.2 – Call Takers per Shift ................................................................................................................. 40 6.2.3 – Call Volume .............................................................................................................................. 41

6.3 KEY PERFORMANCE INDICATORS ................................................................................................................ 41 6.4 DISCUSSION OF RESULTS ........................................................................................................................... 43

6.4.1 Example of Results Obtained ...................................................................................................... 43 6.4.1.1 Example of Use of Results .................................................................................................................... 44

6.4.2 Results by Time Window at 100% Call Volume .......................................................................... 45 6.4.3 Results by Time Window at 115% Call Volume .......................................................................... 51 6.4.4 Summary of Results .................................................................................................................... 54

6.5 COMPARISON OF TIME WINDOW RESULTS TO 24/7 RESULTS .......................................................................... 56 6.5.1 Weekends ................................................................................................................................... 59

6.6 QUESTIONS ANSWERED ............................................................................................................................ 60 6.6.1 Current Sufficiency of Staffing Levels ......................................................................................... 60 6.6.2 Overstaffing and Understaffing.................................................................................................. 60 6.6.3 Sufficiency of Current Staffing levels in the Future ..................................................................... 60 6.6.4 Required Staffing Levels ............................................................................................................. 61

7.0 VALIDATION ..................................................................................................................................... 62

7.1 VALIDATION BY AN EXPERT ........................................................................................................................ 62 7.1.1 Validation of the Simulation Model ............................................................................................ 62 7.1.2 Validation of the Excel Model ..................................................................................................... 62

7.2 VALIDATION BY COMPARING SIMUL8 RESULTS WITH EXCEL-BASED MODEL ......................................................... 63 7.2.1 Validation by Means of Producing Similar Conclusions .............................................................. 63 7.2.2 Validation by Numerical Comparison of Results ........................................................................ 66

8.0 CONCLUSION AND RECOMMENDATIONS ......................................................................................... 68

8.1 SUMMARY ............................................................................................................................................. 68 8.2 CONCLUSION .......................................................................................................................................... 68 8.3 RECOMMENDATIONS ............................................................................................................................... 70

8.3.1 Night Staffing ............................................................................................................................. 70 8.3.2 Day Staffing ................................................................................................................................ 70 8.3.3 Afternoon/Evening Staffing ........................................................................................................ 70 8.3.4 Break Periods .............................................................................................................................. 70 8.3.5 Shift Start Times ......................................................................................................................... 71

9.0 FUTURE WORK .................................................................................................................................. 72

9.1 CHANGING THE SHIFT SCHEDULE ................................................................................................................ 72 9.2 WORKFORCE SCHEDULING ........................................................................................................................ 72 9.3 NON-HOMOGENEOUS WORKFORCE ............................................................................................................ 73

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9.4 SIMUL8 OPTIMIZATION FUNCTION – OPTQUEST ........................................................................................... 73 9.5 INCREASING THE TIME GRANULARITY OF THE ANALYSIS/SEASONALITY ............................................................... 73 9.6 CREATING QUEUES FOR EACH CALL PRIORITY ................................................................................................ 74 9.7 WEEKEND STAFFING LEVELS ...................................................................................................................... 74

BIBLIOGRAPHY ....................................................................................................................................... 76

APPENDIX A: COMPLETE SIMUL8 RESULTS ............................................................................................. 77

APPENDIX B: USER MANUAL FOR SIMUL8 SIMULATION MODEL ............................................................ 92

APPENDIX C: USER MANUAL FOR EXCEL-BASED CALL TAKER MODEL ..................................................... 97

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List of Figures

Figure 1: Process Overview of the Thesis Methodology .................................................... 4

Figure 2: Example of Three Phone Lines at EMS Headquarters ...................................... 12

Figure 3: Example of Hourly Call Instances ..................................................................... 16

Figure 4: Example of Data Points Listings ....................................................................... 16

Figure 5: Example of Best Fit Software Fitting a Distribution ......................................... 17

Figure 6: Example Output for Erlang Parameters for Monday ......................................... 18

Figure 7: Example of Call Duration Determination .......................................................... 19

Figure 8: Average Call Duration for Various Call Types ................................................. 20

Figure 9: Duration of Emergency Calls Distribution ........................................................ 20

Figure 10: Duration of Emergency Calls Distribution in Ten Segments .......................... 21

Figure 11: Example of Call Duration Distribution used for Simul8 ................................. 22

Figure 12: Shift Patterns including Breaks ....................................................................... 28

Figure 13: Image of the Simul8 Model ............................................................................. 29

Figure 14: Image of the Excel Model – Numerical Representation .................................. 34

Figure 15: Image of the Excel Model – Graphical Representation ................................... 35

Figure 16: Image of Excel Model – Call Volume by Hour of the Week .......................... 36

Figure 17: Average Number of Calls, by Hour of Week, Last Three Years ..................... 37

Figure 18: Shift Patterns for Call Takers at EMS Call Centre .......................................... 39

Figure 19: Graph from Excel Model – Minimum Number of Call Takers ....................... 59

Figure 20: Actual (4-2-2-2) Staffing Levels vs. Required Staffing Levels ....................... 64

Figure 21: Actual (6-4-2-2) Staffing Levels vs. Required Staffing Levels ....................... 65

Figure 24: Example of Erlang distribution for calls on Monday from 8am-9am ............. 99

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List of Tables

Table 1: Clock Time Windows Examined ........................................................................ 40

Table 2: Number of Call Takers per Shift – Actual and Simulated .................................. 40

Table 3: Example Results Tableau as seen in Simul8 ....................................................... 43

Table 4: Results 0000- 0200 / 4-[2,3,4]-2-2 / 100% Call Volume .................................... 45

Table 5: Results 0200-0700 / 4-[2,3,4,5,6]-2-2 / 100% Call Volume ............................... 47

Table 6: Results 0700-1000 / [4,5,6]-2-2-2 / 100% Call Volume ..................................... 48

Table 7: Results 1000-1400 / [4,5,6]-2-[3,4,5]-2 / 100% Call Volume ............................ 48

Table 8: Results 1400-1900 / [4,5]-2-[2,3]-2 / 100% Call Volume .................................. 49

Table 9: Results 1900-2400 / 4-[2,3,4]-[2,3]-[2,3] / 100% Call Volume ......................... 49

Table 10: Results 0200-0230 / 4-[2,3,4,5,6,7]-2-2 / 100% Call Volume .......................... 50

Table 11: Results 0000-0200 / 4-[2,3,4]-2-2 / 115% Call Volume ................................... 51


Table 13: Results 0700-1000 / [4,5,6]-2-2-2 / 115% Call Volume ................................... 52

Table 14: Results 1000-1400 / [4,5,6]-2-[2,3,4]-2 / 115% Call Volume .......................... 53

Table 15: Results 1400-1900 / [4,5,6]-2-2-[2,3] / 115% Volume ..................................... 53

Table 16: Results 1900-2400 / 4-[2.3]-2-2 / 115% Call Volume ...................................... 54


Table 18: Minimum Staffing Level where at least 95% of Calls Answered Within 10

Seconds.............................................................................................................................. 55

Table 19: Shift Pattern versus Percentage of Calls Answered within Ten Seconds ......... 58

Table 20: Numerical Comparison of Excel and Simul8 Staffing Levels .......................... 66

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List of Thesis Project Responsibilities

Site Visits to EMS: Both

Simulation Model: Gillian Chin

Excel Model: Jason Coke

Analysis of Simul8 results: Both

Writing: Both, as described in thesis body

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1.0 Introduction

(written by Gillian Chin)

1.1 Purpose

The purpose of this document is to account for the work completed, the methodology

used and the results obtained for this fourth year Industrial Engineering thesis project. This thesis

project primarily focused on performing analyses of the call-taking functionality of the Toronto

EMS Call Centre, and was conducted through the construction and examination of simulation

models using Simul8 software. The goal is to optimize the staffing levels of call takers by striking

a balance between allowing for excess capacity, yet not wasting resources needlessly.

1.2 Background

The Toronto Emergency Medical Service (EMS) is currently the largest service of its

kind in Canada. It is one of the largest and most comprehensive pre-hospital emergency care

systems in the world and it is internationally recognized for its system’s design. It is the primary

source of both emergency and non-emergency medical transportation within the GTA, servicing a

population of approximately 3.5 million people, addressing over 425,000 9-1-1 calls and

transporting 165,000 medical patients each year [1]. It currently employs approximately 1,125

personnel, 76% of which are paramedics, while the remainder is composed of management,

dispatchers and support staff. In addition, there are currently 45 EMS stations posted throughout

the Toronto area, with ambulances reporting an average utilization rate of 45.29% in servicing the

public and covering over 650 square kilometres [1].

Toronto EMS is also responsible for providing 24 hr emergency and non-emergency pre-

hospital medical care, as well as offering transportation to individuals experiencing injury or

illness, fostering the motto of “People Helping People”. More specifically, the Mission Statement

of Toronto EMS is as follows:

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“Toronto Emergency Medical Services (EMS) exists to safeguard the quality of life in our city through the provision of outstanding ambulance-based health services, responding in particular to medical emergencies and to special needs of vulnerable communities through mobile health care.”[2]

1.3 Motivation

The Toronto Emergency Medical Service represents an integral part of the region’s health

care delivery system, and is viewed as an essential public safety service for the community and its

citizens. In order to maintain its level of service and responsibilities to the GTA, it is continually

attempting to improve and integrate its systems with other public services, so as to remain as

efficient and effective as possible. However, from the years 2000 to 2006, the number of medical

emergencies in Toronto per year rose dramatically from 188,000 to 215,000 [1]. Despite budget

increases during this period, the general consensus among EMS personnel was that the level of

effectiveness experienced by the increased investment into their division did not adequately

relieve the pressures and burdens felt by related resources and personnel [3]. It was also believed

that an exhaustive and in-depth analysis of the overall system was required, in order to suggest

possible redesign changes that would improve effectiveness and thoroughly address these issues

of service levels in conjunction with operator utilization.

While holistic and system wide improvements are in need of implementation in order to

regain optimal service levels and response times, the focus of this thesis will be limited

specifically to the EMS Call Centre. This is primarily due to the time versus complexity

constraints, and hence the focus will specifically be on the call-taking functionality. When a

medical emergency occurs, the Call Centre is the first point of contact for a victim or witness.

Being able to rapidly assess the caller’s situation and the medical severity of the victim, as well as

being able to dispatch an appropriate response unit based on location and readiness, in as little

time as possible, is a matter of life and death.

Since the focus of this project is on the call-taking functionality at the EMS Call Centre, a

thorough understanding of the process and system is required. For example, it is important to

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know that in addition to answering emergency 9-1-1 calls, call takers in the Call Centre must also

respond to administrative and non-emergency calls. An added complexity to the analysis is that

the call takers are unaware beforehand which kind of call they will be receiving, as it is entirely

possible that emergency calls are received from non-emergency lines, and vice versa.

The pattern of incoming calls is also an important aspect to study; the amount of calls being

received by EMS personnel on weekdays tends to follow a fairly stable daily pattern that rises and

falls quite predictably [3]. A similar pattern can be found for weekends. Despite the “average”

amount of calls being stable and predictable, on any given day there will be random variations,

and effects such as the weather or civic events can have an effect on the number of calls.

Therefore, given that EMS needs to ensure that call demand during peak hours (10am – 2pm on

weekdays) is met by a sufficient supply of call takers, much thought needs to put into the staffing

levels of call takers, and therefore this is one of the primary objectives of this thesis project.

1.4 Objectives

The primary objective of this thesis is to build a simulation model that accurately reflects

the EMS Call Centre, its incoming calls and the rates at which they are processed by call takers.

In order to achieve this, two other objectives must be completed. First, historical call data must be

analyzed to determine the frequency and duration of calls. These are used as input parameters for

the simulation model. The simulation is then run for a number of trials while varying parameters

like the number of call takers on duty and the volume of incoming calls. After the results of the

simulation have been obtained, they must be validated. This occurs in two ways; first, they are

validated by experts at EMS. Secondly, they are validated mathematically by an Excel-based

model of the Call Centre. A flow chart of the process can be seen in Figure 1 below.

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Figure 1: Process Overview of the Thesis Methodology

Once the model has been validated, the results will be analyzed and the most important

questions will be answered. These questions are as follows:

� Are current staffing levels sufficient to meet current call demand?

� Are there times when the Call Centre is overstaffed or understaffed?

� If so, what should the number of call takers be during any given hour of the week?

� Are current staffing levels sufficient to meet an increase in call volume in the future?

� If not, what staffing levels will be required to meet that increase in volume?

In addition to answering these questions, given the current data available and the current

simulation model, the intention is to provide EMS with a workable simulation model that can be

used in future analyses.

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2.0 Literature Review


The use of simulation and queuing theory in analyzing large scale complex systems has

been well-documented in a diverse group of industries and applications. This section of the thesis

report will thoroughly discuss and review the concepts behind the topics of simulation, queuing

theory, and their applications specifically to call centres, as well as justify their validity and worth

to the analysis in this thesis. It will also document theories and concepts taken from academic and

industrial sources, in an attempt to develop a more comprehensive description of the associated

topics, and further highlight their usefulness to the analysis performed.

2.1 The Use of Simulation for Modeling/Analysis

Simulation has been proven useful in numerous industries and under a wide variety of

applications, providing insight into complex, organizational behaviour and developing

improvements in real world operations without imposing any real changes to the system or

physical structure. When analyzing a system, in some instances many simulation models can be

solved using algorithmic or mathematical means; however, there are many cases where the

system is so inherently complex, it makes it virtually impossible to solve to optimality through

mathematical measures. In the latter case, computer simulation provides an invaluable tool in

analyzing complex systems for the behaviour of the system can be imitated over time. As a result,

data can be analyzed and collected as if the real system were being observed and this also allows

for alternate configurations of the existing system to be assessed, without any real changes being

made to the physical structure [4]. Historically, a model is defined as “a representation of a

system for the purpose of studying the system” [4]. Furthermore, a simulation model is defined as

“the imitation of the operation of a real-world process or system over time. Whether done by

hand or on a computer, simulation involves the generation of an artificial history of a system, and

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the observation of the artificial history to draw inferences concerning the operating characteristics

of the real system” [4]. Thus, through the method of constructing and analyzing system behaviour

through careful investigation, logical inferences can be made that may improve system

performance and/or design, without altering the present system, making simulation a very

powerful tool.

Though simulation has been proven to be a very effective and powerful tool in a diverse

group of industries, its use must be carefully regulated. Situations where simulation is deemed

appropriate for use are listed below [4]:

1. Simulation enables the study of and experimentation with the internal interactions of a

complex system or of a subsystem within a complex system

2. Informational, organizational and environmental changes can be simulated and the effect

of these alterations on the model’s behaviour can be observed

3. The knowledge gained in designing a simulation model may be of great value toward

suggesting improvement in the system under investigation

4. By changing simulation inputs and observing the resulting outputs, valuable insight may

be obtained into which variables are most important and how variables interact

5. Simulation can be used as a pedagogical device to reinforce analytical solution

methodologies

6. Simulation can be used to experiment with new designs or policies prior to

implementation, so as to prepare for what may happen

7. Simulation can be used to verify analytical solutions

8. By simulating different capabilities for machines, requirements can be determined

9. Simulation models designed for training allow learning without the cost and disruption of

on-the-job learning

10. The modern system is so complex that the interactions can be treated only through

simulation

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Although simulation has been termed a powerful and revolutionary tool in systems

management, there are many caveats associated with its use. The primary disadvantages of

simulation are as follows [4]:

1. Model building requires special training

2. Simulation results can be difficult to interpret

3. Simulation modeling and analysis can be time consuming and expensive

4. Simulation is used in some cases when an analytical solution is possible or even

preferable

2.2 Queuing Theory as a Viable Methodology of Data Representation

While it may be quite difficult to formulate and conceptualize complex systems in terms

of their overall structure and description, it is often quite possible to develop a representative

mathematical model of mostly any complex system, which allows the general characteristics and

behaviour to be assessed and analyzed, in an attempt to determine insightful observations and

useful information. This can typically be performed through the use of queuing theory. Queuing

Theory is often used to describe the “more specialized mathematical theory of waiting lines, or

queues,” [5] and has been proven useful in many simulation models. It is also typically associated

with business strategies or plans associated with allocating resources with the express objective of

providing a level of service. Coincidentally, “the subject of queuing theory has been developed

largely in the context of telephone traffic engineering” [5] which is particularly useful in the

analysis of this thesis where “such models can be defined in terms of three characteristics: the

input process, the service mechanism, and the queue discipline” [5]. The input process defines

how arrivals are structured and what mathematical model can be used to imitate its behaviour,

meaning it specifies the population of the individuals who represent potential clients of the

system, also known as the calling population. The service mechanism determines how each

activity or item is handled once they are selected from the queue, and the queue discipline

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determines the manner in which the activities or items are processed. For example, the service

mechanism may specify the service time or the amount of time it takes to service a customer,

while queue disciple will determine the way and order they are served, such as: FIFO (First In,

First Out) and LIFO (Last In, First Out) [5].

The use of queuing theory also allows for the calculation of key performance measures or

deliverables, which evaluates the efficiency and effectiveness of the underlying system by

calculating, for example, the average wait time in the system. Conversely however, queuing

theory does have its limitations. Many of the assumptions made in queuing theory may not reflect

the real world environment and may adversely affect calculations: for example, infinite capacity

in a queue or infinite calling populations. Therefore, care must be taken when utilizing queuing

theory as a means of data representation, to ensure that any simplifying assumptions made do not

sufficiently distort the analysis, creating false data and incorrect conclusions.

2.3 Simulation and Queuing Theory in relation to Call Centres

In terms of the use of queuing theory and call centres, most of the preliminary study and

research in queuing theory was associated with telephone systems. For example, one of the first

published articles pertaining to queuing theory was a paper published by Johannsen in 1907 titled

“Waiting Times and Number of Calls” [6]. Furthermore, in terms of the importance and long

range impact in queuing theory, A.K. Erlang published a series of articles starting from 1909 and

covering the next 20 years. “Erlang himself was a Danish telephone engineer who developed his

ideas while trying to solve the operational problems of the telephone system” [6]. Thus, much of

the initial research into queuing theory was developed and associated with real world problems or

applications that were experienced at the time of invention, many problems of which were

associated with the telephone or communication system.

By definition, a call centre “constitutes a set of resources which enable the delivery of

service over the telephone […] Typically, call centre goals are formulated as the provision of

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service at a given quality, subject to a specific budget” [7]. Specifically, queues in service

operations are a vital measure and diagnostic tool for determining quality levels. Customers

derive their experience from their time spent in the queue and/or system; as stated by Koole and

Mandelbaum, queues in service play the same role as inventory does in manufacturing. Queues

can be used as an indicator for control and improvement opportunities, and they “provide

unbiased quantifiable measures in terms of performance, which is relatively easy to monitor and

goals are naturally formed” [7].

However, over the next few years, call centres will continue to grow exponentially in

operational complexity. Call volume will undoubtedly escalate, with increasing complex

schedules, routing rules and different operator skills. While mathematical models have proven

useful in coordinating call centres, simulation has begun to play a more important role in

scheduling and call centre management. As specified by Mehrotra et al, there are three major

ways that simulation can be utilized within the call centre industry, to supplement the

mathematical analysis:

Traditional Simulation Analysis: A simulation model is built to analyze a specific operation.

Embedded Application: Routing: These include a routing simulation to provide insight about the

impact of different decisions when it comes to the routing design.

Embedded Application: Agent Scheduling: This is a complex scheduling problem, which

becomes even more complex when both calls and agents are non-homogenous. [8]

The analysis that was performed for this specific thesis project is a hybrid between a

Traditional Simulation Analysis, and the Embedded Application: Agent Scheduling. While the

simulation model that was built focuses on the specific operation of call-taking, we are concerned

with the scheduling of homogenous agents required to service different classes of calls.

Another example of simulation use in call centres would be the case at Bell Canada. Bell

was concerned with maintaining a positive relationship with their customers, and viewed this

relationship as an essential component, critical to their success. The analysis was prompted more

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as an improvement measure, and was initiated internally. The result from the analysis was a

greater understanding of the system, and improved operations through the discovery of

bottlenecks and redundant work. In conclusion, Bell managed to build an operational business

design and decision tool that analyzed and measured customer experience, through the use of

simulation at their call centres [9]. Thus, simulation is a vital tool in analyzing complex systems,

such as a call centre, and has certain advantages over mathematical methods, and renders itself a

vital component to achieving improvements in operations.

2.4 Simulation and Queuing Theory in relation to Emergency Services

There have been many documented cases of the use of simulation and queuing theory

applications in the emergency services sector. Many, however, are focused on the holistic view of

emergency services rather than addressing the issue of call centres specifically. In addition, the

majority of published academic articles on call centres to date seem to be restricted to

applications in commercial environments rather than of public service. However, given these

circumstances, the use of simulation and queuing theory in the emergency sector is an established

practice. For example, Wafik H. Iskander presented a paper at the 1989 Winter Simulation

Conference, on “Simulation Modeling for Emergency Medical Service Systems”. This paper

presented the development of a simulation model that was built with the express purpose of

aiding EMS planners and managers with a tool that would aid in planning their operations as well

as making decisions. This simulation model analyzed the entire process of delivering emergency

care, from receipt of call to return of ambulance to centre after transporting patients. The result of

the paper was that the developed simulation model was flexible enough to be adapted to any

geographical area, and could aid in pivotal decision making and operations planning [10]. E.S.

Savas also published a paper in the Management Science Journal in 1969, titled “Simulation and

Cost-Effectiveness Analysis of New York’s Ambulance Service”. The general ideas of the paper

were to highlight the advantages of using computer simulation to analyze possible improvements

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that could result from changing the number and locations of ambulances, and from which a cost

effectiveness analysis could be produced to analyze the changes. The result of the simulation

would be a lower operating cost for the emergency services, given optimal positioning of the

ambulance fleet, as well as a decision making tool for determining specific numbers and locations

of ambulances, that could be used on an iterative basis [11]. Finally, Syi Su and Chung-Liang

Shih published an article titled “Modeling an Emergency Medical Service System using

Computer Simulation”, which documented the use and advantages of utilizing computer

simulation in the Taipei Emergency Medical Service System, looking at the entire process of pre-

hospital care. In summary, the simulation managed to identify several areas in need of

improvement for delivering greater emergency care, in a method that was low cost, low risk and

easily operated [12]. Therefore, simulation has been well-documented in the emergency medical

service system, and implemented with great success in many cases, making simulation a powerful

tool for public service.

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3.0 Methodology

(written by Gillian Chin and Jason Coke)

This chapter describes the methodology used for the analysis of the EMS Call Centre,

and is separated into three major components. The first is the data analysis performed to construct

the simulation parameters. The second is the entry of those parameters into the simulation model

and the running of the model. The third is the use of an Excel scenario sheet which attempts to

validate the results found in the simulation model. As complete descriptions of the simulation

model and Excel model are discussed in Chapter 4 and Chapter 5, respectively, they will not be

discussed in depth in this chapter.

3.1 Description of Call Receiving System

The following sections describe the process of call reception at the EMS Call Centre.

3.1.1 Description of General System for Call Receiving:

The current system is set up with a total of 277 lines on which calls to the EMS Centre

can be received, 12 of which are designated 9-1-1 emergency lines. These 9-1-1 emergency lines

are divided into two separate trunks, each of which is designated to a specific area of Toronto;

one trunk for the East and one trunk for the West. Each line out of the total 277 is set up with two

separate priority codes, forming a two-dimensional priority scheme. To explain these two

schemes, an example is shown in Figure 2 below:

LinesFromAVTECDB

Line+umber Line+ame LineType EmergencyLine Priority ACDPriority

182 TOR FD 2 PHONE

05-28

P Y 7 7

196 397-9590 PHONE 03-

07

P Y 5 7

197 397-9591 PHONE 04-

07

P Y 8 7

Figure 2: Example of Three Phone Lines at EMS Headquarters

13

The ACD Priority number is the number designated for the Automatic Call Distribution

(ACD) priority, and this is the more influential priority number of the pair. The AVTEC

computer, which initially receives and prioritizes the calls, will first assess the ACD Priority

number, which in all three cases is “7”. Within the ACD Priority Code “7”, there is an additional

priority scheme, the Priority Number. The Priority Number determines the sequence within an

assigned priority code, with the assumption that the higher the number, the greater the priority of

the call. These priority codes are attributed to these lines upon installation, and have nothing to do

with the actual content of the call (whether emergency, administrative or non-emergency).

Therefore, for this example, the sequence would be as follows: line 197, line 182, line 196. Line

197 is at the front of the queue, following the assumption that first, the call with the higher

priority ACD number, and second, the call with the higher priority code within that specific ACD

priority number, will be moved to the front of the queue.

For a call that is coming from the 9-1-1 Police Headquarters, there are 12 emergency

lines, as mentioned before. If a call is sent to an available line from the 9-1-1 headquarters, it will

ring for 5 seconds, and then switch to another line within the same trunk; Lines 1-5 and 12 are in

the first trunk, while Lines 6-11 are in the second trunk. These calls are not “answered” by a

human operator at EMS, but rather by the computer system known as AVTEC. AVTEC will

receive the call, and based on the line it entered from, priority levels will be assessed and the call

is placed within the queue that waits for an available call taker. If none of the twelve 9-1-1

emergency lines are available, the call is rejected.

Once a call is placed within the queue to the call takers, it waits in line until answered by

the next available call taker; synonymous to the queue in a bank. (View Figure 13: Image of the

Simul8 Model for a complete diagram of the call receiving system) Once a call is answered, the

call taker assesses the medical status of the victim and assigns a priority level, ranging from alpha

(lowest) to echo (highest). The call information is then sent to the dispatch area. In dispatch, there

14

are four dispatchers, one for each quadrant of the city. The call will be sent to the appropriate

dispatcher based on the location of the call. At that point, the dispatcher will then determine the

closest available ambulance unit and route it to the scene. If a call has been received by the

AVTEC computer, yet has not been answered by an available call-taker within ten seconds, each

line at every station within the Call Centre will begin ringing, including that of non-ACD staff:

for example, dispatchers. Therefore, for this analysis, the service goal that the model will attempt

to attain will be represented by this ten second interval after entry.

Throughout the field of systems modeling, simulation is known to be a valid

mathematical modeling and analysis tool that has been proven valuable to many industry

situations, including that of modeling EMS systems.

3.1.2 Description of ACD Specific Call Receiving System

The focus of this thesis project is to analyze the staffing requirements for the call taking

functionality and propose optimal, or near optimal results, with the primary objective of

maximizing the number of calls processed within a specific service level given a minimal amount

of workers. For this specific analysis, the service level that the model hopes to attain would be

that each call is answered by a call taker within ten seconds of receipt into the system. Therefore,

the focus of this thesis project is restricted only to the calls that call-takers will be responsible for,

and these are represented under the heading ACD or Automatic Call Distribution lines. These

lines are composed of the 12 emergency lines, discussed in the previous section, as well as 20

additional lines, that are primarily used for paramedics who are on scene and request aid, or for

scheduled patient transfer. As the scope of the analysis is limited to the responsibilities of the call

takers, which are confined to ACD specific lines, the simulation will be restricted to these lines

alone.

15

3.2 Data Analysis

This section describes the methodology used for determining the distribution of calls for

each hour of the week and hence their inter-arrival rates, as well as the call duration and call

distribution for each of the call types.

3.2.1 Incoming Call Distributions/Inter-arrival Rates EMS provided an Access database with details on all calls to EMS between July 2005

and September 2007. The initial format given was not very usable, so modification was

necessary. Primarily, it was required to change the date formats so that analysis could be

performed succinctly based on the dates. It was, however, found that entire blocks of dates were

missing from the database. Of the 802 total days between the start and end dates in the data, 83

days were missing, bringing the total number of days with data to a reduced total of 719.

The data was broken into three tables based on the three call types: ACD_2N

(Administrative), ACD_2Y_7_8 (Non-Emergency) and ACD_9 (Emergency). Using SQL

queries, these tables were further broken down based on day of week and hour of day. Then, the

total number of calls in each hour was determined. The final result was a table exported into

Excel that listed the number of calls in an hour, for every instance of that hour in the two year

period. An example of this can be seen in Figure 3 below.

16

Figure 3: Example of Hourly Call Instances

Once sorting had been performed to group all hours of each day together, the result was a

list of approximately 100 values that represented the spread of values for the number of calls in

each hour of the week. Due to the fact that some of the dates within the time range were missing,

not every hour of the week had as much as 100 values for it. The spread was between 79 and 105,

with the vast majority of the cases having more than 95 values. In any case, having this many data

points for each hour means there is a sufficient amount of data from which to create a valid

distribution.

An example of the listing of the number of these data points can be seen in Figure 4

below. The variability of these values increased greatly for ACD_2N and ACD_2Y_7_8 calls as

compared to ACD_9 calls, which were quite stable.

Figure 4: Example of Data Points Listings

17

The Best Fit 4.5 (Student version) software package was then used to determine the

distribution parameters for incoming calls. That is to say, for each call type, day and hour, the

data points were fitted to an Erlang distribution and the parameters alpha and beta were

calculated. An example of this can be seen in Figure 5 below.

Figure 5: Example of Best Fit Software Fitting a Distribution

A primary assumption of this model is that the call arrivals follow an Erlang distribution,

but as [4] has shown, incoming calls to a call centre do tend towards and Erlang distribution.

In addition to the three separate call types (administrative, non-emergency and

emergency), distributions were also fit to an overall call arrival rate that grouped all calls

together, rather than breaking them up. This was performed to allow for the possibility of using

only one call type that would have the properties of all three types combined into one. Thus, the

final output of this analysis was a chart that included, for each hour of the week, parameters alpha

and beta. Below, Figure 6 shows the final output for the amalgamated call type, as well as the

three specific call types and their distribution parameters for Monday only.

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TOTAL CALLS Erlang Distribution ACD_9 Erlang Distribution ACD_2N Erlang Distribution ACD_2Y_7_8 Erlang Distribution

Day of Week Hour alpha beta Day of Week Hour alpha beta Day of Week Hour alpha beta Day of Week Hour alpha beta

Mon 0 8 3.7929 Mon 0 8 2.6029 Mon 0 2 2.5053 Mon 0 2 2.4505

Mon 1 9 3.1166 Mon 1 8 2.3664 Mon 1 3 1.8035 Mon 1 2 2.1224

Mon 2 6 4.2712 Mon 2 6 3.0768 Mon 2 2 2.1845 Mon 2 2 1.8791

Mon 3 8 2.7120 Mon 3 8 1.8419 Mon 3 2 2.1989 Mon 3 2 1.6722

Mon 4 6 3.2092 Mon 4 6 2.1356 Mon 4 2 1.9551 Mon 4 2 1.6978

Mon 5 6 3.4167 Mon 5 7 1.9958 Mon 5 2 2.1607 Mon 5 2 1.6467

Mon 6 11 2.7540 Mon 6 8 1.9596 Mon 6 6 1.7199 Mon 6 2 2.6064

Mon 7 13 3.5505 Mon 7 11 2.0455 Mon 7 5 3.4000 Mon 7 4 1.9100

Mon 8 10 5.8725 Mon 8 9 3.4346 Mon 8 5 4.3216 Mon 8 3 2.4455

Mon 9 12 5.8513 Mon 9 12 2.9845 Mon 9 8 3.4459 Mon 9 3 2.7288

Mon 10 15 5.0033 Mon 10 23 1.6147 Mon 10 6 4.9688 Mon 10 4 2.4175

Mon 11 12 6.1988 Mon 11 13 2.9513 Mon 11 6 4.5122 Mon 11 4 2.5975

Mon 12 12 6.3366 Mon 12 25 2.9830 Mon 12 7 3.5104 Mon 12 3 3.6403

Mon 13 16 4.6293 Mon 13 17 2.3145 Mon 13 8 3.2174 Mon 13 4 2.5900

Mon 14 17 4.3674 Mon 14 16 2.4130 Mon 14 6 4.5653 Mon 14 4 2.4208

Mon 15 15 4.7641 Mon 15 15 2.5320 Mon 15 6 3.9553 Mon 15 4 2.7279

Mon 16 17 4.0969 Mon 16 15 2.4876 Mon 16 7 3.2474 Mon 16 5 2.1644

Mon 17 19 3.3473 Mon 17 14 2.9492 Mon 17 7 2.4698 Mon 17 4 2.5172

Mon 18 15 4.1373 Mon 18 15 2.4196 Mon 18 6 2.8986 Mon 18 3 3.1056

Mon 19 17 3.3535 Mon 19 17 2.0346 Mon 19 5 2.5794 Mon 19 3 3.3856

Mon 20 15 3.6085 Mon 20 15 2.2373 Mon 20 4 3.2320 Mon 20 3 2.7582

Mon 21 17 2.9487 Mon 21 15 2.0647 Mon 21 4 2.9768 Mon 21 3 2.6633

Mon 22 14 3.4041 Mon 22 14 2.1043 Mon 22 4 2.6418 Mon 22 3 2.7157

Mon 23 15 2.5484 Mon 23 13 1.9563 Mon 23 2 3.4531 Mon 23 3 2.1837

Figure 6: Example Output for Erlang Parameters for Monday

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These values were then used as the input parameters for the simulation model to describe

the rate of incoming calls of each call type.

3.2.2 Call Durations The other necessary variable obtained from the data was the average duration of the

various call types. Because Microsoft Access does not offer an “average” function for time

lengths (only integers and floats) it was necessary to copy the database table with call durations

into Excel, and then break it into minutes and seconds, sum them appropriately and then calculate

the average duration. It was specified by EMS that all calls longer than 9:59 were to be ignored,

so this was taken into account when taking the average. Figure 7 below shows the calculation of

the average duration times for emergency calls.

Figure 7: Example of Call Duration Determination

The final results of this analysis are shown in Figure 8 below. Because there are many

more ACD_9 (emergency) calls than other types, the greater duration for these calls has a large

impact on the average duration for the total calls.

20

ACD_Type Minutes Seconds Total_Seconds Total_Instances

ACD_2N 1 39.683 99.683 224957

ACD_2Y_7_8 1 6.994 66.994 130609

ACD_9 2 31.703 151.703 506081

Total_Calls 2 5.185 125.185 861647 Figure 8: Average Call Duration for Various Call Types

3.2.3 Call Duration Distribution For the sake of determining which service times would be used in the simulation model,

it was initially assumed that the average could be used. However, upon later reflection and input

from EMS, it was decided that the duration of each call type is distributed in real life, and that the

model should reflect this. When using an Excel add-in tool called XLSTAT 2008, it became

readily apparent that even within each call type, there were bimodal distributions for call

duration, as shown in Figure 9.

Figure 9: Duration of Emergency Calls Distribution

Various probability distribution types were used for attempting to fit the data; however,

each type had a p-value of less than 0.0001. This bimodalism of EMS calls is likely because even

within each call type, there will be two or more “types” of calls. That is to say, one type is a quick

call to briefly inform EMS about something, while another is a longer call that requires more

interaction between the two parties. Alternatively, this bimodalism can be linked back to the

21

concept of line installation. Upon installation of each line, specific ACD priority numbers are

assigned to each line, and the AVTEC computer uses these pre-specified values to assess the

priority level of each call being received. It is entirely possible that the content of the call may not

reflect the line it arrives on. For example, a non-emergency call could arrive on a pre-specified

emergency line, and this could account for the bimodal function of the call duration.

None of the probability distributions fit the reality of these call distributions, but a

method of representing the call duration was still required for the simulation model. Thus, it was

decided to break the call length into ten equal segments, and using XLSTAT, determine the

probability of being within each segment. Figure 10 shows the distribution of call duration once

broken down into ten segments.

Figure 10: Duration of Emergency Calls Distribution in Ten Segments

For the sake of representing these values in the simulation model, a custom distribution

was used based on the probabilities taken from Figure 10, while the midpoint of each of the ten

segments was taken as the duration.

22

3.3 Entering Data into the Simulation Model

This section describes how the data analysis performed resulted in the input parameters

for the simulation model.

3.3.1 Incoming Call Distributions/Inter-arrival Rates

The results of the data analysis for the call distribution were the Erlang parameters: alpha

and beta, as shown in Figure 6. The complete data includes three sets of 168 alpha and 168 beta

parameters. This is exported from an Excel file into a spreadsheet within the “Information Store”

in the Simul8 file, where the values are then read and applied appropriately for any given hour.

3.3.2 Call Duration Distribution

The resulting outcome of section 3.2.3, where the call duration was broken into ten

segments, is a table like what is shown in Figure 11 below.

probability call length (sec)

22 30

22 90

25 150

15 210

6.5 270

3.5 330

2 390

2 450

1 510

1 570

Figure 11: Example of Call Duration Distribution used for Simul8

Simul8 allows for the use of custom distributions when specifying the duration of work

items at work stations. Thus, a table as shown above in Figure 11 was copied into the custom

distribution list for each of the three call types.

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4.0 The Simulation Model


This chapter describes the how the call receiving system was first understood, and

then constructed in a simulation model.

4.1 Data Development: Learning the System

A great deal of the initial effort for this thesis was spent at the Toronto EMS Call Centre,

learning the system, and ensuring that the final simulation would indeed reflect reality. Most of

these efforts have been documented in Chapter 3. Adrian, a data analyst at Toronto EMS,

compiled several Microsoft Access tables that provided the majority of the data used in the

analysis, and many consultations were held to ensure that the data was in a fashion that was

relevant, tractable, and easily understood. Several visits were also conducted at the Toronto EMS

Call Centre with Dave Lyons, the manager of the Toronto EMS System Control Centre Design

Project, to ensure that the scope of the project was appropriate, as well as discussing the general

system structure. The following topics were discussed:

• ACD (Automatic Call Distribution) Priority Categories

• Pre-emptive Call Priorities

• Physical Structure: e.g. number of physical stations available

• Current Shift and Break Patterns

• Current Staffing Levels

Determining this information was essential to constructing the simulation model and performing

the analysis, and had significant impact on the development and construction of the final model.

24

14.2 Physical Structure of the Simulation

The following section describes the parts of the simulation model, an image of which is

shown in Figure 13.

4.2.1 Call Arrivals

The current system structure for the EMS Call Centre was constructed in the simulation

model. There are three priorities of incoming calls that a call taker will receive, each of which

will have different inter-arrival times based on the hour of the week, thus creating three different

entry points for the simulation model. Label “A” in Figure 13 highlights the three entry points.

Calls of priorities one, two and three correspond to, respectively, administrative, non-emergency

and emergency calls.

Entry points signify a pool from which arrivals may enter the system, and each entry

point has a different arrival distribution. These arrival distributions change every hour, and the

method of determining these distributions was discussed in detail in Chapter 3.

4.2.2 Queue for Incoming Calls

Another aspect that was incorporated in the simulation model was the concept of a single

queue after the point of entry. The queue is indicated by label “B” in Figure 13. Every arrival into

the system enters a single queue, where each call is sorted and sequenced based firstly on the

priority level, then on the arrival time. If both a work centre (label “C” in Figure 13) and a call

taker resource (label “D” in Figure 13) are available, the call at the front of the queue will leave

the line and enter the work station. After being processed at the call centre, the call will proceed

to an exit node (label “E” in Figure 13), and the call is considered complete. While there is

additional processing that usually takes place after the call has been handled by a call taker, these

25

actions are considered to be outside of the scope of analysis. Therefore, after each call is

processed by the call taker, the call is considered to be complete.

4.2.3 Call Stations

There are currently nine available call stations in place; however, as of June 2008, a tenth

station will be installed. As this model was built with the intention of being used for future

investigations, the tenth station was incorporated in this simulation model and analysis. Call

stations are noted in Figure 13 by the label “C”. Call stations can process calls only when a

resource (that is, a call taker, label “D” in Figure 13) is present at that station.

4.3 Visual Logic Commands

Once the surface structure had been constructed in the simulation model, visual logic was

used to coordinate and enforce specific regulations held by Toronto EMS.

4.3.1 Inter-Arrival Rate Parameter Reset

The simulation analysis was performed at the time scale granularity of examining each

hour of the week. As the inter-arrival rate parameters were subject to change for this level of time

granularity, it was necessary to incorporate visual logic that would reset the inter-arrival rate

parameters for each of the three priority calls, at the start of every hour of the week. The updates

performed for the distribution parameter values for the inter-arrival rates were based on the values

obtained from data analysis performed on the historical data. Chapter 3 discusses explicitly the

methods of data analysis used.

The methodology of updating the parameters is as follows. An “Information Store”, in

simulation vernacular, or a spreadsheet, is located within the simulation model that records the

parameters of the Erlang distribution for each call priority based on the hour of the week. Upon

the start of each hour, the visual logic code reads the spreadsheet for the appropriate hour and

updates the inter-arrival parameters, depending on the call priority and the hour of the week. The

26

work centre labeled “Bouncer” (see label “F” in Figure 13) is the means for achieving time-based

parameter changes.

4.3.2 Call Durations

Since each of the three call types is not subject to changing duration distributions, it is

assumed that each priority level call has one distribution that specifies its total duration.

Therefore, the call duration of each priority level call does not need to be reset based on the hour

of the week, which is necessary in the case of inter-arrival rates. To incorporate the historical data

into the simulation model, a customized probability distribution profile was created for each

priority level call type, specifying the duration of each priority level call. Upon arrival into the

work centre, visual logic code assesses the priority level of the incoming call, and extracts the

corresponding duration distribution for processing the call. A detailed explanation of the method

used to obtain these distributions is given in Chapter 3.

4.3.3 Pre-emptive Call Priorities

Due to the inherent nature of the EMS Call Centre, a call taker has the option of putting a

lower priority call on hold to answer a call with a higher priority level. Therefore, the

methodology used to map this into the simulation model was to develop visual logic code to

enforce the call pre-emption specifications. Specifically, when a call of priority level two or three

enters the queue, the visual logic code creates a counter that will parse through each work centre

to determine if all work centres are busy. If there is an available call station (or work centre), then

the code “breaks” or does not perform any further actions, because the queue is already organized

according to priority levels; therefore the call with a higher priority level (level two or three) is

moved to the head of the queue, and taken into the available work centre. If all work centres are

in use, however, a counter would then parse through each work centre to determine the priority

level of the call being processed. The call stations are searched in ascending order, and upon

discovery of a work centre processing a call of priority level one, the call will be removed from

27

the work centre and moved back to the queue, while the higher priority call would be moved into

the newly available work centre for call processing. This methodology was enforced through the

use of several loops and counters within the visual logic code.

4.3.4 Incorporating Shift Patterns Due to the existing structure of shift patterns currently in place at Toronto EMS Call

Centre, incorporating the shift patterns into the simulation model in an efficient approach became

very difficult as there were no mathematical patterns that could be exploited for coding purposes.

It also became quite difficult to sequence lunch breaks, as the duration of the entire lunch break

across all staff was dependent on the total number at the start of the shift, in conjunction with the

number allowed to go on break together.

Therefore, incorporating existing shift patterns into the simulation model, in a method

that would be economical, became quite difficult. The objective was to build a simulation with

the current shift patterns in place, but one that facilitated future changes so that the simulation

will still be a valuable tool upon such an event. Thus, the methodology used was to break the

entire 24 hour day into 15 minute intervals, and specify how many call takers are available within

each 15 minute interval.

To specify the number of call takers available during each 15 minute interval, a

supplementary Excel sheet was used. In the spreadsheet, the number of call takers staffed on all

shifts is inputted, and taking into account the break pattern, the number of total call takers is

calculated for each 15 minute interval. This sheet can be seen below in Figure 12.

28

Figure 12: Shift Patterns including Breaks

Based on the staff levels specified in the supplementary Excel sheet, the numbers

representing the sum are be imported into an “Information Store”, or spreadsheet, within the

simulation model titled “Shift Patterns”. The visual logic accesses the spreadsheet at the start of

the simulation, and populates the shift patterns for the call taker resource. The shift pattern for the

call taker resource is also be broken down into 15 minute intervals, to ensure that the correct

correspondence of granularity in terms of worker availability.

29

Figure 13: Image of the Simul8 Model

A

D

B

C

F

E

30

5.0 The Excel Model

(written by Jason Coke)

5.1 Rationale for the need of an Excel Model

At the outset of this thesis project, it was determined that a means of validating the

simulation model, previously discussed in Chapter 4, would be to construct an Excel-based

model. This model, while not capable of having work entry points, queues, or work stations,

would rather calculate mathematically the number of call takers required to meet a certain

call volume for each hour of the week.

5.2 Methodology for Constructing the Excel Model

The method of obtaining the Erlang parameters alpha and beta for each hour of the

week was thoroughly discussed in Chapter 3. These values are imported into Excel and

matched appropriately to each hour of the week. Using the gamma inverse function in Excel,

GAMMAINV (probability, alpha, beta), it was possible to calculate the arrival rate of each

call type for each hour of the week. A definition of the term “probability” in this context is

provided below in section 5.3.1.2. Excel has no specific Erlang function, but since Erlang

distributions are a special kind of Gamma distribution, it is possible to use the gamma inverse

function as a direct substitute.

Then, based on the average duration of each call type, the fictitious value “fractional

amount of call takers” required to meet call volume in each hour is calculated. The sum of

these fractional amounts from each call type was then calculated to represent the total amount

of fractional call takers required for each hour. Finally, this fractional amount is rounded up

31

to the nearest whole number, and this value is taken as the minimum number of call takers

required to be available and answering calls, during any given hour of the week.

5.2.1 The Numerical Representation

The Excel model has two representations for the staffing levels; numerical and

graphical. The numerical representation can be seen in Figure 14, and the columns and cells

listed below are best understood by referring to that figure. The day of week and hour of day

are shown in columns F and G, respectively. Columns AC and AD, respectively, show the

alpha and beta parameters for that hour. Column AE shows the calculated arrival rate of calls

per hour based on the average duration, shown in cell AE5, for the non-emergency call type,

as labeled in cell AE4. The other two call types, administrative and emergency, are shown in

previous columns, but due to space viewing limitations, they could not all be shown in one

image. Column AF shows the fractional amount of call takers required to handle the volume

of calls of the non-emergency call type. Column AH then shows the fractional sum of the

three call types, and column AI shows the integer value once it has been rounded up to the

nearest whole integer. The values in this column are the primary output of the Excel model.

5.2.2 The Graphical Representation

The graphical representation of the model output is shown in Figure 15. It is a bar

chart that shows the number of call takers required for each hour of the week. While the

numerical representation is more useful for performing analysis, the graphical representation

is more helpful for the user to observe changes in staffing levels as the model parameters are

varied.

32

5.3 Functionality

The Excel-based model is not static; various functionalities are included to allow the

user some flexibility in their modeling efforts.

5.3.1 Parameter Changes

The three parameters of desired busy rate, probability, and total call volume may be

varied within this mode. In Figure 14, the cells with parameter values are in the top left

corner in bright green.

5.3.1.1 Desired Busy Rate

The desired busy rate is the fraction of time that call takers are talking on the phone.

The default is set to 0.65, meaning they are on the phone 65% of the time. The remaining

35% is excess capacity.

One shortcoming of the model is that this value cannot change depending on the hour

of the week. In reality, this busy rate would change depending on time of day and staffing

levels. However, if the assumption that EMS always wants the same amount of excess

capacity holds true, then this value is valid.

5.3.1.2 Probability

The probability value represents the percentile in the Erlang distribution for call

volume for a given hour, from which the number of calls arriving is selected. For example, a

value of 0.5 will calculate the arrival rate from the 50th percentile of historical calls for each

hour.

33

5.3.1.3 Total Call Volume

The total call volume determines the overall number calls arriving to the system.

When set to 100%, the exact average of incoming calls based on historical data is used. This

functionality was included so that a future increase in call volume could be simulated.

5.3.2 Two Methods of Adjusting Call Volume

To allow for more flexibility in this parameter, two methods of adjusting call volume

are possible.

5.3.2.1 Adjusting by Total Call Volume

The call volume for all hours of the week can be adjusted simultaneously by

changing the value in cell G5 (Figure 14) from the default of 100% to any other value. For

example, simulating an increase in call volume of 10% is achieved by entering “110%” into

the cell.

5.3.2.2 Adjusting Call Volume by Hour of the Week

In order to simulate a crisis or some other event that would cause a large increase in

call volume over a period of one or more hours, functionality was included to allow for these

events. For example, in Figure 16, the call volume for Saturday at 6pm was increased to

150% of normal volume to simulate a large accident. Immediately, the graph on the left will

reflect this change by showing that two extra call takers would be required at 6pm on

Saturday.

34

Figure 14: Image of the Excel Model – +umerical Representation

35

Figure 15: Image of the Excel Model – Graphical Representation

36

Figure 16: Image of Excel Model – Call Volume by Hour of the Week

37

6.0 Analysis of Results


This chapter will present and analyze the results obtained from the Simul8 trials.

6.1 – Analysis Overview

As seen in Figure 17 below, the average number of calls arriving in any given hour of

the week varies by time of day and day of week. Thus, it was necessary to run the simulation

model numerous times while changing certain variables for each trial.

Figure 17: Average +umber of Calls, by Hour of Week, Last Three Years

All final results were obtained using the “Trial” function in Simul8. The Trial

function allows each simulation to be run 20-30 times, and then the averages, along with the

99% confidence intervals, were taken for each key performance indicator once the trial was

complete. On average, each trial lasted about one minute in real time, but each of the 20-30

simulations in a trial ran for the duration of a full month (30.417 days).

Although Figure 17 above shows a distinct difference in call volume between

weekdays and weekends, EMS has the same shift patterns seven days a week. Since any staff

level that could accommodate weekday volume would most certainly be able to

38

accommodate weekend volume, the model did not focus specifically on weekends.

Additionally, it was found that trying to model only the weekends in Simul8 would require

extensive visual logic coding; unfortunately, there is no easy way to run a model for Saturday

and Sunday only. However, since it is considered valuable to consider weekends, section

6.5.1 does document analysis performed specifically on weekends; additionally, a section in

Future Work (Chapter 9) is devoted to discussion of this topic.

The variables changed are as follows:

� The time of day

� The number of call takers on each shift

� The volume of calls

Specifics on how these variables were changed are discussed in the subsequent section.

6.2 – Variables

This section describes how and why the three variables specified above were chosen

and manipulated for the simulation trials.

6.2.1 – Time of Day

Call taker shifts at EMS always run for 12 hours. There are four shifts per day; 7am-

7pm, 7pm-7am, 11am-11pm and 2pm-2am. Figure 18, below, shows the active time of day in

green for each shift.

39

Figure 18: Shift Patterns for Call Takers at EMS Call Centre

For most hours of the day, there are two or more shifts on duty at the same time.

However, the red bar to the right of the chart indicates that from 2am-10am, there is only one

shift on duty within this block of time. Because the start or end of a shift will have a

significant impact on the total number of call takers in a given hour, simulations were run for

segments of each day depending both on shift start and end times, as well as call volume.

This was a logical decision because having time windows that overlap both shift changes and

rapid changes in call volume would produce a meaningless “average” result. 10am-2pm is the

period of time each day when the highest volume of calls are received, so it was examined,

even though a new shift starts at 11am.

In addition, many trials were run with each simulation lasting one full month (30.417

days) for 24 hours each day, including weekends. While the results within a specified time

range, for example, 7am-10am, are more meaningful since they focus in on “bottleneck”

times of the day, the 24 hour trials were used to add robustness and validity to the results by

40

comparing the trends found in those results with the trends found in the restricted time

windows.

Table 1 below shows the clock times of day that were simulated:

Clock Time Windows

12am-2am

2am-7am

7am-10am

10am-2pm

2pm-7pm

7pm-12am

2am-2:30am *

Table 1: Clock Time Windows Examined

* 2am-2:30am was looked at closely because it appeared to be a time that caused a serious bottleneck

for incoming calls.

By segmenting the clock time and taking advantage of the shift start and end times,

the number of combinations of variables are reduced. This is because, when a shift is not

within the time window being examined, it remains a static value, as it has no bearing on the

results of that time period.

6.2.2 – Call Takers per Shift

The number of call takers on each shift was varied appropriately, depending on the

time window that was being simulated. The current range for the number of call takers on

each shift is shown in Table 2 below. Also shown are the numbers of call takers used in at

least one of the simulation trials.

+umber of Call Takers Per Shift

Shift 7am-7pm 7pm-7am 11am-

11pm

2pm-2am

Number of call takers (actual) 4-6 2-3 2 2

Simulated 4-7 2-6 2-4 2-4

Table 2: +umber of Call Takers per Shift – Actual and Simulated

41

The total possible number of combinations of call-takers was 4*5*3*3 = 180.

However, by intelligently using time windows in the clock time, it was possible to drastically

reduce the number of combinations. Also, by observing the intermediate results and trends in

the key performance indicators, it was possible to limit the combinations along a particular

axis, or shift, when, for example, 99% or more of calls were being answered in less than ten

seconds, which is the critical time limit used in the EMS Call Centre.

6.2.3 – Call Volume

Analysis showed that over the past three years, EMS has received an average of

about 36,000 calls per month, with a standard deviation of 2,367. The simulation trials were

run in two batches. First, they were run at 100% of the average volume, or 36,000 calls per

month. Second, they were run at 115%, or 41,400 calls per month. This was performed to

simulate a future increase in the average volume of calls. The value of 115% was an arbitrary

selection; however, assuming a normal distribution for the number of calls in a month, five

percent of the time, values should be more than 40,734, which represent two standard

deviations above the mean. Indeed, the highest single monthly value in the database was for

August of 2006, with 40,256 calls. These calculations were made without including the

months that did not have complete data.

6.3 Key Performance Indicators

The following measures are the key performance indicators that were used in

analyzing the results of the trials. In Simul8, the averages, as well as the 99% confidence

interval for each measure were presented in the results.

42

� Maximum Queue Size. The largest number of simulation objects (calls) that were

waiting in queue to be answered by a call taker at one time.

� Maximum Queuing Time (in minutes). The longest time that any call had to wait in

the queue.

� Average Queuing Time (in minutes). The average queue time of all calls.

� Average (non-zero) Queuing Time (in minutes). The average time spent in the queue,

counting only calls that had to wait for a call taker to become available.

� % Queued less than time limit. The percentage of calls that were answered in less

than 10 seconds.

� Utilization %. The percentage of time that a call taker is on the phone, averaged over

all call takers and all hours of the simulation duration.

All of the above performance measures can be used to gain an understanding of the

system for a given set of variables. However, two Key Performance Indicators (KPIs) are the

most critical to this analysis and must be examined: the percentage of calls that queued for

less than ten seconds, and the utilization rate of the call takers. Of these, the former is

considered to be the most important, and therefore will be given preference over the latter

when proposing recommendations.

It should also be noted that while the maximum queue time can be a valuable

indicator of system performance, some of the results indicate an extraordinarily high wait

times that are much longer than the actual span of the simulation. First, it is uncertain how the

software calculates these values, and second, the values may be influenced by the visual logic

code that enforces pre-emptive priority for emergency and non emergency calls over

43

administrative calls. In the cases where there are obviously too few call takers to handle

incoming call volume, as the queue grows, incoming high priority calls will continuously be

pushed to the front of the queue ahead of the lower priority calls. This results in the lower

priority calls remaining in the queue for a considerable time. Thus, this indicator should be

viewed in terms of its magnitude as opposed to its absolute value, and should be viewed in

conjunction with other performance indicators, in order to reach a comprehensive conclusion

about the system.

6.4 Discussion of Results

The following section will present and discuss the results of the simulation trials

performed.

6.4.1 Example of Results Obtained

An example of a results tableau from a simulation trial is shown in Table 3.

Performance Measure -99% Average 99%

Maximum queue size 33.34 36.47 39.59

Maximum Queuing Time (min) 132.36 149.07 165.78

Items Entered 35812.71 35856.10 35899.49

Average Queuing Time (min) 0.93 0.97 1.01

Average (non-zero) Queuing

Time (min) 4.83 4.99 5.15

St Dev of Queuing Time 5.43 5.74 6.05

% Queued less than 10 sec. 82.75 83.05 83.34

Utilization % 46.50 46.65 46.79

Table 3: Example Results Tableau as seen in Simul8

For the purpose of analysis in this thesis, it is assumed that the acceptable level of

service is having 95% of calls answered within ten seconds. In this example trial, the average

values for the two critical KPIs are in bold. 83% of calls were answered in less than ten

seconds, and the call takers were busy answering calls almost 47% of the time. While those

KPIs indicate that on average most calls are answered quickly (83%) and call takers are not

44

over-worked, there are other indicators that should raise a red flag of warning. The maximum

queuing time is 149 minutes, and the average non-zero queuing time is five minutes. Since

the average queuing time is less than one minute, this shows that there must be some periods

of time where the volume of incoming calls greatly exceed the service capacity of the on-duty

call takers.

Thus, the data indicates that there exists a certain degree of disparity between call

demand and call taker supply. These results were returned for a simulation running over 24

hours, seven days a week, and they demonstrate the necessity for further time window

analysis that will further explore the details of the system and determine specifically when the

bottlenecks occur.

6.4.1.1 Example of Use of Results

The determination of periods of time where severe inconsistencies between incoming

call volume and call taker availability are observed will lead to recommendations being made

regarding the number of call takers to staff at certain hours of the day. For example, if it is

found that the average utilization rate of call takers is 20% between 2pm and 3pm, the

recommendation would be to remove one of the call takers from a shift that covers that time

of day. By contrast, if 75% of calls between 1am and 2am are not answered within ten

seconds (below the acceptable standard of 95%), and the call takers have a 98% busy rate, the

recommendation would be to add at least one more call taker.

In the simulation trials, the effects of adding or removing call takers are readily

available and are measured in further trials where fewer or more call takers are used.

45

Depending on what EMS deems as acceptable threshold values for the two main KPIs, the

optimal staffing level can be chosen through thorough examination of this data.

Therefore, this is the method used for analyzing data, resolving the objectives of this

thesis, and suggesting appropriate recommendations.

6.4.2 Results by Time Window at 100% Call Volume

Below are the results assuming 100% volume, delineated by time window and

specific shift patterns. Shift patterns are in the format of x-x-x-x, for example, 5-4-3-2 means

five staff on the 7am-7pm shift, four on the 7pm-7am shift, three on the 11am-11pm shift and

two on the 2pm-2am shift. The minimum staffing level is generally assumed to be 4-2-2-2,

and represents the current standard shift pattern at the EMS Call Centre.

12am-2am 4-2-2-2 4-3-2-2 4-4-2-2

Performance Measure Average Average Average



Items Entered 35856.10 35869.45 35869.45



Time (min) 3.32 1.24 0.65



Utilization % 48.47 41.18 33.14

Table 4: Results 0000- 0200 / 4-[2,3,4]-2-2 / 100% Call Volume

Table 4 shows that the minimum staffing level of 4-2-2-2 is insufficient to meet call

demand between 12am-2am because the averages for maximum queue size and queuing time

are unacceptably high. Only 78.7% of calls are answered within ten seconds. Adding a third

call taker on the 7pm-7am shift increases this performance measure to 92%, while a fourth

increases it further to 98.5%.

46

Despite the minimum staffing level having a low performance measure of 78.7%, the

utilization rate is relatively low. This suggests that there is some variation within this two-

hour period in terms of the equivalence between call volume and call taker availability, likely

due to call takers going on breaks. For example, between 12am and 12:30am, both the 7pm-

7am and 2pm-2am have a break. Therefore, with two people on each shift, that results in only

two out of four call takers able to answer the phones. Thus during this half hour, the two call

takers are unable to keep pace with incoming calls; the queue continues to grow, and hence

the high maximum queue size and maximum queuing time is relatively large. When the two

call takers return from their breaks, the queue quickly diminishes and this results in excess

capacity among the call takers, hence the low utilization rate. The utilization rate takes into

account the average busy rate only for the time that call takers are not on break, so it is

weighted disproportionately towards the low end because the highest service rates occur

when no one is on break. For example, with four call takers on duty, when two go on break,

the other two are very busy. When all breaks are finished, the four are not very busy. Hence,

the utilization rate is calculated as: two times the busiest rate plus four times the idle rate.

This observation should be kept in mind for all of the seemingly low utilization rates

presented in this report. It also represents another reason as to why the percentage of calls

answered within ten seconds is considered to be of greater importance than call taker

utilization.

47

2am to 7am 4-2-2-2 4-3-2-2 4-4-2-2 4-5-2-2 4-6-2-2

Performance Measure Average Average Average Average Average

Maximum queue size 2641.83 129.10 37.10 18.75 7.70

Maximum Queuing Time (min) 20556.27 507.68 106.59 49.90 15.79

Items Entered 35856.10 35869.45 35869.45 35869.45 35869.45

Average Queuing Time (min) 1085.84 10.59 1.19 0.20 0.03


Time (min) 1089.93 16.46 3.83 1.56 0.76

St Dev of Queuing Time 3530.00 37.40 4.87 1.31 0.29

% Queued less than 10 sec. 3.45 42.01 73.10 89.35 97.02

Utilization % 99.81 70.78 53.08 42.47 35.38

Table 5: Results 0200-0700 / 4-[2,3,4,5,6]-2-2 / 100% Call Volume

From 2am-7am, only the night shift (7pm-7am) is present at this time, so the only

staffing variable to change is the number of call takers on that shift. Trials were run with two,

three, four, five and six call takers on this shift. With only two call takers, there is an

extremely high utilization rate, maximum queue size, average queue time, and only 3.45% of

calls were answered within ten seconds. The likely cause of these results is that when the

2pm-2am shift leaves at 2am, only two 7pm-7am call takers remain. However, because of the

break pattern, from 2am-3am and 4:30am-5:30am, only one of the two call takers is on duty.

During these times, the single call taker cannot keep up with the volume of calls and therefore

the queue continually grows.

With each addition of an extra call taker on the 7pm-7am shift, the performance

measures exhibit drastic improvements. The first instance of relatively acceptable

performance measures occurs when five call takers are on this shift, with 89% of calls

answered in less than ten seconds. However, it is questionable as to whether EMS would

48

want one call out of ten to wait above the time limit, thus the simulation was run again with

six call takers, and the performance measure jumped to a highly acceptable value of 97%.

7am to 10am 4-2-2-2 5-2-2-2 6-2-2-2




Time (min) 3.40 1.49 0.74


Utilization % 50.88 40.75 33.96

Table 6: Results 0700-1000 / [4,5,6]-2-2-2 / 100% Call Volume

The period from 7am-10am also has only one shift present, and thus only one

variable to consider. With four call takers, the concern is that only 77% of calls are answered

within ten seconds. This measure is 91% and 98% for five and six call takers, respectively,

and while 91% is deemed to be moderately acceptable, having six call takers clearly has a

substantially positive impact.

10am to 2pm 4-2-2-2 4-2-3-2 5-2-2-2 6-2-2-2

Performance Measure Average Average Average Average

Maximum queue size 8.85 7.65 5.70 3.90

Average Queuing Time (min) 0.03 0.02 0.01 0.00

% Queued less than 10 sec. 96.56 98.36 98.89 99.74

Utilization % 37.76 33.15 31.97 27.73

Table 7: Results 1000-1400 / [4,5,6]-2-[3,4,5]-2 / 100% Call Volume

Table 7 shows that even at the minimum staffing level of 4-2-2-2, performance

measures are acceptable, with 96.5% of calls answered within ten seconds. Adding a third

call taker to the 11am-11pm shift then makes that value 98.4%. Having five or six call takers

on the 7am-7pm shift, regardless of other shift levels, guarantees a performance level of

about 99% or higher. Although all call taker combinations of four, five or six on the 7am-

7pm shift and three, four or five on the 11am-11pm shift were run in trials, not all the results

49

of the remaining combinations are shown because they are fairly redundant in that they all

have extremely high performance measures in the range greater than 99.0%. 6-2-4-2, for

example, answers 99.96% of calls in less than ten seconds.

2pm to 7pm 4-2-2-2 4-2-2-3 5-2-2-2






Time (min) 0.44 0.33 0.34


Utilization % 26.96 23.59 23.92

Table 8: Results 1400-1900 / [4,5]-2-[2,3]-2 / 100% Call Volume

Table 8 shows that from 2pm-7pm, even with the minimum staffing level of 4-2-2-2,

99.86% of all calls are answered. Additions to any of the day or evening shifts result in even

higher values. It should be noted however, that the addition of a 2pm-2am shift member is

marginally more valuable than adding a 7am-7pm call taker.

In general, the number of incoming calls is falling steadily during this time of the

day, yet there are always three shifts on duty simultaneously, so it is very easy to meet

demand.

7pm-12am 4-2-2-2 4-3-2-2 4-4-2-2




Time (min) 3.12 1.16 1.01


Utilization % 36.89 30.89 27.16

Table 9: Results 1900-2400 / 4-[2,3,4]-[2,3]-[2,3] / 100% Call Volume

50

Table 9 shows that from 7pm-12am, with the minimum staffing level on duty, less

than 90% of calls are answered within ten seconds. Adding a call taker to either the 7pm-7am

shift or 2pm-2am shift proves slightly more beneficial than to the 11am-11pm shift, however,

this could be because the arbitrary time window runs until midnight, one hour after the 11pm

shift ends.

2am-2:30am 4-2-2-2 4-3-2-2 4-4-2-2 4-5-2-2 4-6-2-2 4-7-2-2

Performance Measure Average Average Average Average Average Average

Maximum queue size 18551.0 284.20 284.20 32.00 9.90 9.90

Maximum Queuing Time (min) 8200.78 1033.64 1033.64 120.97 23.62 23.62

Average Queuing Time (min) 4126.47 62.92 62.92 0.65 0.05 0.05


Time (min) 4136.04 74.15 74.15 2.23 0.80 0.80

St Dev of Queuing Time 2376.93 150.68 150.68 3.58 0.42 0.42

% Queued less than 10 sec. 0.28 21.36 21.36 75.83 95.02 95.02

Utilization % 99.85 85.03 85.03 56.59 42.47 42.47

Table 10: Results 0200-0230 / 4-[2,3,4,5,6,7]-2-2 / 100% Call Volume

The period from 2am-2:30am was examined in great detail because it appeared to be

somewhat of a bottleneck in terms of meeting call demand. This appears to be the case

because at 2am, the 2pm-2am shift is finished, leaving only the 7pm-7am shift. Compounding

the problem, the 7pm-7am shift has a scheduled break starting at 2am. The results for three

and four, as well as six and seven call takers are the same because if three are on duty, one

will go on break at 2am, whereas if four are on duty then two will go on break together

(leaving the same number of available call takers). A similar situation exists for six and seven

call takers.

Anything less than five call takers leads to extraordinarily high queue sizes and wait

times. Having six call takers gives the first moderately acceptable performance measures.

51

6.4.3 Results by Time Window at 115% Call Volume

In this section, a 15% increase in call volume has been introduced to the simulations.

This is to simulate both the possibility of an increased call volume over time (a shift of the

mean), or the possibility of a high-volume month by the natural variance of call volume (a

month where the call volume is more than two standard deviations above the mean).

12am-2am 4-2-2-2 4-3-2-2 4-4-2-2




Items Entered 41230.25 41232.00 41232.00



Time (min) 4.36 1.66 0.75



Utilization % 55.74 47.32 38.07

Table 11: Results 0000-0200 / 4-[2,3,4]-2-2 / 115% Call Volume

Table 11 shows that with a 15% increase in call volume, having two or three call takers

on the 7pm-7am shift results in too few (70% and 86.6%, respectively) calls being answered

in ten seconds or less from 12am-2am. Having four call takers on that shift is the minimum

acceptable staffing level. It should also be noted that while Table 4, which represents the

same time window but at 100% call volume, has just under 35,900 items entered, the 15%

increase here has raised the number of monthly calls to over 41,200.

2am-7am 4-2-2-2 4-3-2-2 4-4-2-2 4-5-2-2 4-6-2-2 4-7-2-2






Time (min) 2054.46 53.73 6.12 2.23 0.89 0.75



Utilization % 99.93 81.38 60.97 48.77 40.64 34.84


52

Table 12 indicates that with a 15% increase in call volume, having only two or three

call takers on the 7pm-7am shift would be disastrous, with exceedingly high queue sizes and

wait times. Even having four call takers produces poor results, with only 61% of calls being

answered within ten seconds. This is a time period in the day when only one shift is on duty,

and if call volume were to increase by 15%, EMS would need to drastically increase the

number of call takers available during this time.

It should also be noted that of the five hour period from 2am-7am, the total amount of

break time will vary between two hours and three hours, depending on the total number of

call takers. Therefore, to state that four call takers are on duty is somewhat deceptive; all four

call takers will be available for only two of the five hours, and during the other three hours

there will be either two or three people actively taking calls.

7am-10am 4-2-2-2 5-2-2-2 6-2-2-2 7-2-2-2

Performance Measure Average Average Average Average

Maximum Queuing Time (min) 130.79 66.78 19.80 14.2565

Average Queuing Time (min) 2.12 0.38 0.06 0.02124

% Queued less than 10 sec. 66.36 85.48 95.24 97.8976

Utilization % 58.48 46.82 39.01 33.4362

Table 13: Results 0700-1000 / [4,5,6]-2-2-2 / 115% Call Volume

From 7am-10am at 115% call volume, four or five call takers are insufficient to meet

the call demand. Depending on the threshold that EMS deems acceptable, the 95%

performance measure that six call takers produce may or may not be enough. This is the

second time window where only one shift is on duty; therefore, any breaks taken will have a

large impact on the actual number of call takers available.

53

10am-2pm 4-2-2-2 5-2-2-2 6-2-2-2 4-2-3-2 4-2-4-2 5-2-3-2






Time (min) 0.90 0.71 0.48 0.78 0.82 0.71



Utilization % 43.38 36.74 31.85 38.08 33.93 36.74

Table 14: Results 1000-1400 / [4,5,6]-2-[2,3,4]-2 / 115% Call Volume

Table 14 shows that only the minimum staffing level is below acceptable

performance levels. The addition of just one call taker to either the 7am-7pm shift or 11am-

11pm shift immediately brings service levels up a sufficient degree.

Essentially, this indicates that if, in the future there is a 15% increase in call volume

to EMS, then the “new” minimum staffing level should become 5-2-2-2.

2pm-7pm 4-2-2-2 4-2-2-3 5-2-2-2




Time (min) 0.45 0.40 0.41


Utilization % 30.98 27.11 27.48

Table 15: Results 1400-1900 / [4,5,6]-2-2-[2,3] / 115% Volume

Similar to the results found at 100% call volume, Table 15 indicates that even the

minimum staffing level can easily meet call demand in the period from 2pm-7pm. This is

likely because the three shifts on duty at this time have eight call takers in total, minus those

that are on break, and call demand is steadily falling from the mid-day peak. Thus, even at the

minimum staffing level, the call centre has excess capacity during this time.

54

7pm-12am 4-2-2-2 4-3-2-2 4-4-2-2



Average Queuing Time 0.68 0.10 0.06


Utilization % 42.39 35.48 31.22

Table 16: Results 1900-2400 / 4-[2.3]-2-2 / 115% Call Volume

Table 16 shows that even a minimum staffing level is sufficient to meet call demand

in this time. Increasing the 7pm-7am shift by one call taker gives a marginal improvement

(99.25% versus 98.47%) in the primary performance measure, but the extra call taker is not

necessary.

2am-2:30am 4-2-2-2 4-3-2-2 4-4-2-2 4-5-2-2 4-6-2-2 4-7-2-2






Time (min) 6408.38 230.74 230.74 4.99 0.94 0.94


Utilization % 99.92 97.65 97.65 65.02 48.77 48.77


At 115% call volume, the performance measures for 2am-2:30am are very poor for

less than six call takers. At 2am, the 2pm-2am shift leaves, and the break time for the 7pm-

7am shift starts. Even with five call takers on duty, only three remain to answer calls, and this

is insufficient to meet the call volume. If call volume does increase by 15% in the future, then

EMS would need to begin staffing at least six call takers on the night shift.

6.4.4 Summary of Results

Throughout sections 5.3.2 and 5.3.3, a variety of results are presented that reflect the

performance of the EMS Call Centre at various times of day, staffing levels and incoming

call volumes. The primary performance measure used was the percentage of calls that were

55

answered within ten seconds. The second most important measure, utilization rate of the call

takers, was found to be skewed to the low end for values that were not already very high.

This is likely because it is calculated as an average rate that could include both the very busy

times and very idle times which occur as a result of call takers going on or returning from

their breaks, except idle times occur when more call takers are present, so the “low” busy rate

is multiplied by a greater number of call takers. Thus, it was not viewed as an equally

valuable measure, except when it indicated extremely high utilization rates.

Call taker breaks had a very high impact on the service levels of the call centre. In the

periods from 2am-7am and 7am-10am, only one shift is on duty at a time; therefore, the break

times often left too few call takers available to handle the incoming call volume.

Minimum Staffing Level for which at least 95% of Calls are Answered Within 10 Seconds

12am-2am 2am-7am 7am-10am 10am-2pm 2pm-7pm 7pm-12am 2am-2:30am

100% call

volume 4-4-2-2 4-6-2-2 6-2-2-2 4-2-2-2 4-2-2-2 4-3-2-2 4-6-2-2

115% call

volume 4-4-2-2 4-6-2-2* 6-2-2-2

5-2-2-2 or

4-2-3-2 4-2-2-2 4-4-2-2 > 4-7-2-2

Existing

Staff Level 4-[2,3]-2-2 4-[2.3]-2-2 [4,5,6]-2-2-2 [4,5,6]-2-2-2 [4,5,6]-2-2-2 4-[2,3]-2-2 4-[2,3]-2-2

Table 18: Minimum Staffing Level where at least 95% of Calls Answered Within 10 Seconds

* 4-6-2-2 gives a performance measure of 94%

Table 18 shows that with the current average call volume, existing staffing levels are

sufficient from 7am to midnight if six (not four or five) call takers are on the 7am to 7pm

shift, and if three call takers (not two) are on the 7pm to 7am shift. The 11am to 11pm and

2pm to 2am shifts are sufficiently staffed with two call takers each, and although these

simulations did not test for less than two per shift, it may well be the case that not both call

takers are needed on both these shifts.

56

From 12am-7am, however, Table 18 shows that current staffing levels are

insufficient. The simulations indicate that at least six call takers are needed for the 7pm-7am

shift to meet demand, particularly for the period from 2am-7am.

If call volume were to increase 15%, the period from 10am-2pm would need one

additional call taker for either the 7am-7pm shift or the 11am-11pm shift. This need,

however, is dominated by the period from 7am-10am, when six call takers are needed. Since

the only shift available at this time is 7am-7pm, six call takers are required for that shift, and

will be remain on duty throughout the day. This phenomenon of dominance will be discussed

in the conclusion of this thesis. Additionally, the 7pm-7am shift would require six call takers.

In general, there appears to be sufficient capacity from 10am to 2pm, and excess

capacity from 2pm to 7pm, when three shifts are on duty. However, there appears to be

insufficient staffing for the 7pm to 7am shift. An unexpected result from the simulation trials

is that the period from 2am-7am requires just as many call takers (six) as 7am-10am, even

though call volume is considerably higher in the latter period. One explanation of this could

be that a break occurs immediately at 2am, which could cause an unrecoverable backlog,

since each break period last 1.5 hours with four or more call takers on duty, and there are two

break periods in the five hour period from 2am-7am. Meanwhile, the 7am-7pm shift does not

start break until 8am and has only one 1.5 hour break period before 10am.

6.5 Comparison of Time Window Results to 24/7 Results

While running trials for specific time windows is a valuable method for looking

closely at the effects of parameter changes over smaller periods of time, it is also important to

examine the “larger picture”. In addition to the simulation trials mentioned previously in this

57

chapter, additional trials were conducted for 24 hours a day, seven days a week. Trends found

in the results of these “macro” trials will now be compared to the results of the time window

trials. For the purpose of comparison, only the simulations running at 100% of call volume

are included.

The primary performance measure, the percentage of calls answered within

ten seconds, is the only indicator used for this analysis.

Table 19 below shows the trends for the primary performance measure as the shift

pattern is varied. The far left column shows which shift is being varied, while the inside cells

show the actual shift pattern and the respective performance value, in percent. On the right

are columns for first improvement and second improvement. The first improvement is the

difference of the performance measure, in percent, between the lowest staffing level listed

and the addition of one more call taker. For example, in the first row, 93.09 – 90.50 = 2.59.

The second improvement is the difference between the first addition and the second addition.

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Shift Pattern vs. Percentage of Calls

Answered within 10 Seconds

First

Improvement

Second

Improvement

x-2-2-2 4-2-2-2 5-2-2-2 6-2-2-2 7-2-2-2 2.59 0.93

90.50 93.09 94.02 94.27

4-x-2-2 4-2-2-2 4-3-2-2 4-4-2-2 4.20 0.79

90.50 94.70 95.49

5-x-2-2 5-2-2-2 5-3-2-2 5-4-2-2 4.16 0.87

93.09 97.25 98.12

6-x-2-2 6-2-2-2 6-3-2-2 6-4-2-2 4.22 0.78

94.02 98.24 99.02

4-2-x-2 4-2-2-2 4-2-3-2 4-2-4-2 0.92 0.16

90.50 91.42 91.58

4-2-2-x 4-2-2-2 4-2-2-3 4-2-2-4 1.23 0.13

90.50 91.73 91.86

5-2-2-x 5-2-2-2 5-2-2-3 5-2-2-4 1.28 0.07

93.09 94.37 94.44

Table 19: Shift Pattern versus Percentage of Calls Answered within Ten Seconds

Table 19 indicates similar trends to those found in the time window simulation. The

addition of call takers to the 7pm-7am shift produces the largest increase in performance (the

cells in yellow). The next best improvement, 2.59%, is obtained by adding a call taker to the

7am-7pm shift. Meanwhile, adding call takers to the 11am-11pm or 2pm-2am had little

impact, and, as is shown by the very low values for second improvement (0.16 and 0.13),

virtually no improvement could be made by further additions to these two shifts.

Thus, the 24 hour simulation results are in complete agreement with the time window

results. They both suggest that performance will increase by adding at least one more call

taker to the 7am-7pm shift, and at least one more to the 7pm-7am shift, while the 11am-11pm

and 2pm-2am shifts are already sufficiently staffed.

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6.5.1 Weekends

Although it was not possible to conduct simulations for weekends alone, the Excel-

based model readily accounts for all hours of the week. With the default values of 0.65 for

desired busy rate, 0.9 for probability, and 100% for call volume, Figure 19 below

demonstrates the resulting bar chart for the required number of call takers for each hour of the

week.

Figure 19: Graph from Excel Model – Minimum +umber of Call Takers

Weekends clearly follow a distinctively different trend than weekdays. The

highest number of call takers required for weekends is five, while for all weekdays,

the required value is six. Additionally, the weekends required a minimum of three call

takers during the night, while weekdays require only two as a minimum. Thus,

weekends have lower requirements in the day but higher requirements at night. Given

that the previous analyses suggest a shortage of staffing at night during the week, it is

likely that this shortage becomes even more severe on Friday and Saturday nights.

Thus, it does not seem reasonable to have the same staffing patterns for

weekends as weekdays. Future work will be necessary to establish the proper staffing

requirements for weekends.

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6.6 Questions Answered

In Chapter 1, five questions were posed with regards to staffing levels and the

capabilities of the EMS Call Centre to meet call demand both currently and in the future. For

convenience, they are listed again below.

1) Are current staffing levels sufficient to meet current call demand?

2) Are there times when the Call Centre is overstaffed or understaffed?

3) If so, what should the number of call takers be during any given hour of the week?

4) Are current staffing levels sufficient to meet an increase in call volume in the

future?

5) If not, what staffing levels will be required to meet that increase in volume?

Based on the results found in this chapter, these questions are answered in the sections below.

6.6.1 Current Sufficiency of Staffing Levels

In response to question 1, current staffing levels are sufficient to meet demand during

the mid-morning, afternoon and evening times, however, they are insufficient during the late

night and early morning hours, particularly from 2am-7am.

6.6.2 Overstaffing and Understaffing

In response to question 2, overstaffing occurs from 2pm-7pm, when there are three

shifts concurrently on duty. Even at the minimum staffing level of 4-2-2-2, there is excess

capacity during this time. Understaffing occurs for the 7pm-7am shift and is particularly

noticeable from 2am-7am, once the 2pm-2am shift has left.

6.6.3 Sufficiency of Current Staffing levels in the Future

In response to question 4, if a 15% increase in call volume were to occur in the

future, the current staffing levels would not be sufficient. In particular, there would be too

few call takers during the 7am to 7pm and 7pm to 7am shifts.

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6.6.4 Required Staffing Levels

In response to questions 3 and 5, the required levels of staffing for both current

volume and a future increase of 15% are listed in Table 18. These values are determined

under the assumption that a reasonable target for the primary performance measure is 95% of

calls being answered within ten seconds. If this target value was lowered, then similarly, there

would be a decrease in the staffing numbers determined by the simulation model.

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7.0 Validation


Validation of simulations models is of great importance [4]. Since pivotal decisions

can be made by management on the basis of simulation results, the validity of the model and

accuracy of these results must be subject to intense investigation [4].

Therefore, this chapter discusses validation attempts for the simulation model by

several means. Validation is achieved through two methods; first, by checking with an expert

from Toronto EMS to ensure that the simulation is a valid representation of the real-world

system, and secondly, by comparing the results in the simulation model to those of the Excel-

based model. The results of the Excel-based model were also validated by experts at Toronto

EMS.

7.1 Validation by an Expert

7.1.1 Validation of the Simulation Model

Once the simulation model was fully constructed, a meeting was arranged with Dave

Lyons, Manager of the Toronto EMS System Control Centre Design Project. The model, its

visual logic code and all work paths were fully explored and explained. Mr. Lyons confirmed

that the model is, in fact, a valid representation of the real world system, insofar as the

simulation software allows.

7.1.2 Validation of the Excel Model

The Excel model was examined both by Mr. Lyons and by the call centre supervisory

staff. With the default values of 100% call volume, 65% busy rate for call takers, and a

probability value of 0.9, all EMS staff consulted agreed that the numbers produced were quite

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reasonable and realistic. Thus, while the Excel model is imperfect and limited in its

functionality, it has been validated by showing that the values produced are realistic.

7.2 Validation by comparing Simul8 results with Excel-based Model

One fundamental difference between the Excel-based model and the Simul8 model is

that while it is possible to account for breaks in the Simul8 model, it is not feasible to do so in

the Excel model. The Excel model does not represent the shift staffing levels, but rather the

actual number of call takers who should be at their stations and available to take calls. Since a

direct numerical comparison may not be possible, validation can be achieved if the results

from each model are found to support the same conclusion.

7.2.1 Validation by Means of Producing Similar Conclusions

In Figure 20 below, the blue line shows the actual number of call takers available to

answer calls, taking into account break patterns, and based on staffing levels of 4-2-2-2. The

red line represents the required staffing level based on the default parameters mentioned

above, and was calculated by taking the average of the minimum staffing levels of each hour

of each day from Monday to Thursday. In this figure, values are presented for every 15-

minute section of the day.

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Figure 20: Actual (4-2-2-2) Staffing Levels vs. Required Staffing Levels

Within Figure 20, any area where the red line (required staff) exceeds the blue line

(actual staff, given a 4-2-2-2 pattern) represents a shortage of call takers. Ideally, the blue line

should always be at or above the red line. Similar to the results from Simul8, Figure 20 shows

that the 4-2-2-2 staffing pattern is insufficient to meet call demand from 2am-7am. The gap is

particularly large for 2am-3am, which would certainly produce similar results to the findings

for 2am-2:30am in Table 10: Results 0200-0230 / 4-[2,3,4,5,6,7]-2-2 / 100% Call

Volume. In the afternoon and evening, there is excess capacity, which was also observed

within the Simul8 model. The only discrepancy between the two models is for the period

from 10am to 1pm. In Figure 20, there are clearly too few call takers to meet demand until

1pm, while the Simul8 results suggest that 4-2-2-2 is sufficient for this time period. This

discrepancy likely exists because the parameter for probability in the Excel model was

established as 0.9, meaning the call volume was sampling from the 90th percentile of call

volume. Meanwhile, the Simul8 model takes the mean value from probability 0.5 but samples

anywhere between 0 and 1. Also, the Excel model will tend to estimate the required staff

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level on the higher side for the busiest time of the day, 10am to 2pm, when a relatively low

busy rate, 65% in this case, is chosen. Despite these limitations of the Excel model, the two

models do appear to present similar results.

Figure 21: Actual (6-4-2-2) Staffing Levels vs. Required Staffing Levels

Figure 21 shows the change in the actual levels (the blue line, with staffing level 6-4-

2-2) relative to the required levels (the red line) once four call takers are added to each 24-

hour period; two more starting at 7am and two more starting at 7pm . Like the Simul8 results,

this now indicates that the 6-4-2-2 staffing level is sufficient to meet demand from 2am-7am.

Similar to Figure 20, there is a slight disparity from 8am-1pm, with the supply of call takers

just at or below the required level. The large excess of capacity in the afternoon and evening

hours is readily visible, and it can be seen from this graph that with a few minor 15-30 minute

periods, the 2pm-2am shift is virtually unneeded.

The Excel model thus validates the Simul8 model by producing similar conclusions.

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7.2.2 Validation by Numerical Comparison of Results

It is difficult to make a direct numerical comparison between the Excel and Simul8

models for two reasons. First, the Excel model cannot account for breaks, and in a 24-hour

cycle there are a substantial number of breaks that occur. Second, the Simul8 model provides

the average number of call takers over several hours (a time window), rather than for each

hour. Despite these problems, an attempt to compare the resulting values for the number of

call takers required in each hour is made below in Table 20.

Average Hourly Call Takers Simul8

Adjusted Hour From Excel From Simul8

0 3 5 or 6 3 or 4

1 3 5 or 6 3 or 4

2 2.75 5 or 6 3 or 4

3 2 5 or 6 3 or 4

4 2 5 or 6 3 or 4

5 2 5 or 6 3 or 4

6 3 5 or 6 3 or 4

7 4 6 4

8 5 6 4

9 6 6 4

10 6 8 6

11 6 8 6

12 6 8 6

13 5.75 8 6

14 6 8 6

15 6 8 6

16 6 8 6

17 5.25 8 6

18 5 8 6

19 5 7 5

20 5 7 5

21 4.5 7 5

22 4 7 5

23 4 7 5

Table 20: +umerical Comparison of Excel and Simul8 Staffing Levels

The values in the Simul8 column represent the total staffing level, while the Excel

column represents the number of staff ready and answering calls. As a large generalization, it

can be said that two call takers (from any on-duty shift) are on break in a given hour.

Therefore, subtracting two from the Simul8 column should give the approximate value that

can be used for comparison with the Excel value. When this subtraction is done in the

“Simul8 Adjusted” column, it is not a stretch to conclude that the values are very similar.

67

Therefore, the Excel model validates the Simul8 model by producing comparable

numerical values in terms of actively available call takers.

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8.0 Conclusion and Recommendations


8.1 Summary

In this thesis project, a simulation model of the Toronto EMS Call Centre was

developed and created. The goal of the simulation model was to determine optimal staffing

levels based on historical call volumes, but also to allow for flexibility in terms of call

volume and call taking staff in case there are future changes to these values.

The method of determining if staff volume is sufficient to meet call demand was to

determine if the primary performance measure, the percentage of calls answered within ten

seconds, was within a certain threshold value. For the purpose of this thesis, the threshold

value was assumed to be 95%. If EMS deems that a different value would be more

appropriate, then further simulation analysis may not be necessary; rather, the current results

shown in Appendix A should provide the appropriate staffing level for a given threshold

limit.

Additionally, an Excel model was constructed to determine mathematically what the

minimum number of call takers are to meet the demand of a given hour of the week. The

values found in this model were similar to those found from the simulation trials, thus

validating the Simul8 model.

8.2 Conclusion

In Chapter 1, five questions were posed that represent the essence of this thesis. For

convenience, they are listed once again below.

1) Are current staffing levels sufficient to meet current call demand?

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2) Are there times when the Call Centre is overstaffed or understaffed?

3) If so, what should the number of call takers be during any given hour of the week?

4) Are current staffing levels sufficient to meet an increase in call volume in the

future?

5) If not, what staffing levels will be required to meet that increase in volume?

The results from the simulation show that current staffing levels may not be sufficient

to meet current call volume, and they would almost certainly not be sufficient if call volume

were to increase by 15%. The most severe shortage of call takers was consistently found to be

during the night shift, from 7pm-7am. Currently there are either two or three call takers

staffed on this shift, but the analysis showed that, due to the break patterns, even four call

takers was too few for the period of time from 2am-7am. During this period, only the night

shift is on duty, therefore during the break periods which last for three hours of this five hour

time window, the loss of one or two call takers has a significant impact on service levels.

Analysis showed that having five or six call takers on this shift would improve service to

acceptable levels.

During the day shift from 7am-7pm, four to six call takers are currently staffed.

Although only four call takers are needed for this shift once the 11am-2pm shifts start,

analysis shows that the period from 7am-10am does indeed require six call takers. Thus, this

period of time can be considered a bottleneck and effectively dictates how many call takers

are required for this shift.

The 11am-11pm and 2pm-2am shifts are currently staffed with two call takers each.

The analysis showed that this amount is more than sufficient, even leading to excess capacity.

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8.3 Recommendations

8.3.1 Night Staffing

The first and most important recommendation is to have additional staffing on the

night shift. By having at least four call takers on the 7pm-7am shift, service levels should rise

dramatically, particularly in the period from 2am-7am.

8.3.2 Day Staffing

The next recommendation is to have six call takers on the day shift from 7am-7pm.

This is specifically to meet the call demand prior to the 11am shift arriving.

8.3.3 Afternoon/Evening Staffing

Current staffing levels for the 11am-11pm and 2pm-2am shifts are more than

adequate and allow sufficient excess capacity to deal with a sudden surge in call volume. No

reductions of staffing levels are recommended for these shifts. If it is possible to have only

once call taker on the 2pm shift, then moving the second call taker from the 2pm shift to the

7pm shift would provide a better match between call takers and call volume.

8.3.4 Break Periods

During periods of time when only one shift is on duty, such as from 2am until 10am,

break times have a significant on the ability of the Call Centre to meet call volume. This

simulation model assumes 30 minute break periods and 45 minute lunches. Any reduction in

the break times, say, from 30 minutes to 20 minutes, would have a strong effect on call centre

performance. For example, in the period of time from 2am-7am, a ten minute reduction in

each break period would increase the availability of the full call taking workforce from two

hours to three hours, which in turn would positively impact the key performance measures.

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Furthermore, the number and sequence of call takers going on break at one time

should also be examined. If four call takers are present, two will go on break for the first half

hour, then the third in the second half hour, and then the fourth in the third half hour. For the

breaks that start at 2am for the night shift, it would be more beneficial to have the two call

takers going on break together occupy the third break period, rather than the first. Since call

volume is still falling at this hour, this provides a better match between service and demand.

By contrast, call volume is continually rising during the 8am-9:30am break period of

the day shift, so it is better to have the two call takers take the first break period together, and

the singles take the next two (that is, a 2-1-1 break pattern), assuming there are four in total.

These patterns should be implemented for all shifts that don’t have three, six or nine call

takers. In these cases, the breaks patterns are by default 1-1-1, 2-2-2 or 3-3-3.

8.3.5 Shift Start Times

Although it may not be currently possible to change the starting times of the four call

taker shifts at EMS, some consideration should be given to the possibility. One of the key

discoveries made in the analysis is that caller utilization is often highest during the break

times when only one shift is on duty. Thus, if the shifts were somehow split so that two shifts

were always on duty, this problem could be avoided. Additionally, the 2pm-2am shift was

found to be virtually unneeded, so the staff of this shift would be better starting at a different

time. Further details on changing the shift times are discussed in Future Work in Chapter 9.

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9.0 Future Work


Although the thesis effort has been successfully completed and results have identified

areas of significant improvement, there are still further extensions of the analysis that could

be implemented, if time were permitting. Performing these extensions may provide further

insight and additional depth to the analysis. Areas which could be further explored are as

follows:

9.1 Changing the Shift Schedule

Toronto EMS currently has four shifts for every 24 hours, where each shift is 12

hours in length. The start times are 7am, 11am, 2pm and 7pm. While these start times were

likely chosen to have the best effects on the social and physical well-being of call takers, it

does cause a significant disparity between the incoming call volume and call taker

availability, particularly in the early morning hours. Examinations could be made into:

� different start times

� having two shifts on duty at all times (thus, one shift starting every six hours)

� having five shifts for every 24 hours

� having a split between 8-hour and 12-hour shifts. For example, 8-hour shifts on

weekdays and 12-hour shifts on weekends would minimize the number of

weekends worked

9.2 Workforce Scheduling

The analysis performed to date specifies how many call takers are required to be

available to fulfill a specific service requirement. However, being able to schedule the

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available workers to meet the call volume requirements could bring additional value to

Toronto EMS. Unfortunately, due to time constraints, it was not possible to incorporate

scheduling software as a part of this analysis, but could perhaps be performed as future work.

9.3 Non-homogeneous Workforce

The assumption made in the simulation model was that every worker is viewed as

identical, having the same needs and requirements. However, this is not the case in the real

world; many individuals may have different hours they can work, or different needs on the

job. Constraint-Based Programming is an Operations Research technique that is readily

applied to workforce scheduling problems. Therefore, it can be considered as a tool to help

incorporate the differences between workers in future analysis.

9.4 Simul8 Optimization Function – OptQuest

Simul8 has a built-in optimization function that allows for certain systems or models

to solve to optimality based on specified variables and cost/profit functions. Although such

functionality is very useful, further expertise in the use of Simul8 would be required prior to

beginning this analysis. Costs would need to be associated with call takers, and some form of

penalty cost would be required for calls that were not answered within ten seconds. If

OptQuest were better understood, it would save more time in performing analysis, and

potentially arrive at a better solution.

9.5 Increasing the Time Granularity of the Analysis/Seasonality

The analysis was performed according to a time scale of each hour of the week. This

decision was a basic choice made on behalf of all parties, as a weekly cycle was deemed as

acceptable for the analysis. If a larger time granularity was used, for example, per hour of

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month, perhaps the simulation would more adequately reflect reality and the results of the

analysis may have been improved. This would also allow for the incorporation of seasonality

of call volume, if any exists.

9.6 Creating Queues for each Call Priority

Further queuing analysis could be performed by looking at the results of queuing

times for each call type. Currently, the results are only given for the queue as a whole,

irrespective of the type of calls that may be temporarily stored in the queue. This manner of

analysis would give further insight into what happens in the real system, and segregate the

results for more insightful conclusions for each priority level.

9.7 Weekend Staffing Levels

According to Figure 17: Average Number of Calls, by Hour of Week, Last

Three Years, the volume of calls on the weekends is significantly lower than during

weekdays. Despite this volume difference however, call taker staffing levels remain the same

for weekends as weekdays. Indeed, the Excel model (Figure 19: Graph from Excel Model –

Minimum Number of Call Takers) suggests that weekends need fewer call takers in the day

but more at night in comparison to weekdays. Therefore, analyzing the weekends

independently and in-depth would be a worthwhile effort.

Since Simul8 does not provide an easy way to run simulations for only weekends, it

would be possible to create another simulation model that only has the input parameters for

the weekends. Since Simul8 does include functionality for limiting the number of days in a

week, it could be easily set to run for two days only. While Simul8 would appear to be

running for Monday and Tuesday, it would in fact be running Saturday and Sunday, because

75

the input parameters would be specified for these specific days only. In this manner, it is

possible to model the weekend independently from weekdays.

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Bibliography

[1] Toronto EMS, Overview of Organization, Website: http://www.toronto.ca/ems/

overview/overview.htm: Accessed: September 21, 2007.

[2] Toronto EMS, Overview of Organization: Statistics, Website: http://www.toronto.

ca/ems/overview/statistics.htm: Accessed: September 21, 2007.

[3] David Lyons, Re-Engineering the Process: The Application of Queuing Theory in EMS,

Toronto EMS Communication Centre Design Project, November 2005.

[4] Jerry Banks, John S Carson II, Barry L Nelson, David M Nicol, Discrete Event

Simulation, Fourth ed. , Prentice Hall, 2004.

[5] Robert B Cooper, Introduction to Queuing Theory, Third ed. , North Holland, 1981.

[6] Walter C Giffin, Queuing: Basic Theory and Applications, First ed. , Grid, 1978.

[7] Ger Koole, Avishai Mandelbaum, " Queuing Models of Call Centres: An Introduction,"

Annals of Operations Research, vol. 113, pp. 41-59, 2002.

[8] Vijay Mehrotra, Jason Fama, " Call Centre Simulation Modeling: Methods, Challenges

and Opportunities," Proceedings of the 2003 Winter Simulation Conference, pp. 135-143,

2003.

[9] Oryal Tanir, Richard J Booth, " Call Centre Simulation in Bell Canada," Proceedings of

the 1999 Winter Simulation Conference, pp. 1640-1647, 1999.

[10] Wafik H. Iskander, " Simulation Modeling for Emergency Medical Service Systems,"

Proceedings of the 1989 Winter Simulation Conference, pp. 1107-1111, 1989.

[11] E.S. Savas, " Simulation and Cost-Effectiveness Analysis of New York's Emergency

Ambulance Service," Management Science, vol. 15, no. 12, pp. B608-B627, 1969.

[12] Syi Su, Chung-Liang Shih, " Modeling an Emergency Medical Services System using

Computer Simulation," Information Journal of Medical Informatics, vol. 72, pp. 52-72, 2003.

77

Appendix A: Complete Simul8 Results

This appendix gives the complete results from the Simul8 trials that were run for this

thesis. Section 1 (Time Windows) shows the results that are specific to each defined time

period, and is separated into one part for 100% call volume and another for 115% call

volume. Section 2 shows the results from the simulations that were run for 24 hours a

day, seven days a week. It is also separated into parts based on call volume. Section 2 is

valuable in that it shows the trends that result from varying the number of call takers on

one shift at a time. For example, “x-2-2-2” means that the number of call takers on the

7am-7pm shift were varied while all other shifts remained constant at two call takers.

The structure of the diagrams is as follows:

1. Time Windows

1.1 100% Call Volume

1.1.1 12am-2am

1.1.2 2am-7am

1.1.3 7am-10am

1.1.4 10am-2pm

1.1.5 2pm-7pm

1.1.6 7pm-12am

1.1.7 2am-2:30am


1.2.1 12am-2am

1.2.2 2am-7am

1.2.3 7am-10am

1.2.4 10am-2pm

1.2.5 2pm-7pm

1.2.6 7pm-12am

1.2.7 2am-2:30am

2. 24-Hour Results


2.1.1 Varying x-2-2-2

2.1.2 Varying 4-x-2-2

2.1.3 Varying 5-x-2-2

2.1.4 Varying 6-x-2-2

2.1.5 Varying 4-2-x-2

2.1.6 Varying 4-2-2-x

2.1.7 Varying 5-2-2-x


2.2.1 Varying x-2-2-2

2.2.2 Varying 4-x-2-2

78

2.2.3 Varying 5-x-2-2

2.2.4 Varying 6-x-2-2

2.2.5 Varying 4-2-x-2

2.2.6 Varying 4-2-x-2

2.2.7 Varying 4-2-2-x

2.2.8 Varying 5-2-2-x

Note: the indicator x-x-x-x represents the number of call takers on each of four shifts. For

example, 5-4-3-2 means five call takers for 7am-7pm, four for 7pm-7am, three for 11am-

11pm and two for 2pm-2am.

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12am-2am 100% volume 4-2-2-2 4-3-2-2 4-4-2-2

Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%

Maximum queue size 5.38 6.60 7.82 12.55 14.30 16.05 4.90 5.95 7.00

Maximum Queuing Time 7.91 12.96 18.00 28.10 33.37 38.64 6.57 10.03 13.49

Items Entered 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45

Average Queuing Time 0.01 0.01 0.02 0.11 0.12 0.13 0.01 0.01 0.02

Average (non-zero)

Queuing Time 0.63 0.70 0.77 1.17 1.24 1.32 0.59 0.65 0.71

St Dev of Queuing Time 0.15 0.20 0.24 0.76 0.84 0.92 0.14 0.17 0.20

% Queued less than time

limit 98.39 98.47 98.54 91.94 92.19 92.44 98.39 98.48 98.58

Utilization % 33.01 33.13 33.26 41.03 41.18 41.33 33.02 33.14 33.27

2am-7am 100% volume 4-2-2-2 4-3-2-2 4-4-2-2




Items Entered 35812.71 35856.10 35899.49 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45


Average (non-zero)

Queuing Time 1032.49 1089.93 1147.38 14.97 16.46 17.95 3.63 3.83 4.03


% Queued less than time

limit 3.38 3.45 3.52 41.46 42.01 42.56 72.75 73.10 73.46

Utilization % 99.77 99.81 99.86 70.50 70.78 71.05 52.88 53.08 53.28

2am-7am 100% volume 4-5-2-2 4-6-2-2

Performance Measure -99% Average 99% -99% Average 99%


Maximum Queuing Time 38.58 49.90 61.21 10.49 15.78639 21.08

Items Entered 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45

Average Queuing Time 0.18 0.20 0.23 0.02 0.031 0.035


Time 1.39 1.56 1.72 0.68 0.76 0.84


% Queued less than time limit 89.09 89.35 89.62 96.87 97.02 97.17

Utilization % 42.30 42.47 42.63 35.23 35.38 35.53

Section 1: Results from Time Window Analysis

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7am-10am 100% volume 4-2-2-2 5-2-2-2 6-2-2-2




Items Entered 35812.71 35856.10 35899.49 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45



Time 3.26 3.40 3.54 1.40 1.49 1.59 0.70 0.74 0.79


% Queued less than time limit 76.98 77.26 77.55 90.99 91.17 91.36 97.49 97.58 97.66

Utilization % 50.72 50.88 51.04 40.59 40.75 40.90 33.84 33.96 34.08

10am-2pm 100% volume 4-2-2-2 4-2-3-2 4-2-4-2 5-2-2-2

Performance Measure -99% Average 99% -99% Average 99% -99% Average 99% -99% Average 99%

Maximum queue size 7.07 8.85 10.63 5.71 7.65 9.59 4.88 6.95 9.02 4.62 5.70 6.78

Maximum Queuing Time 13.82 18.86 23.90 7.84 13.38 18.93 7.80 11.75 15.70 6.59 10.21 13.84

Items Entered 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45

Average Queuing Time 0.03 0.03 0.04 0.01 0.02 0.02 0.01 0.01 0.02 0.01 0.01 0.01


Time 0.70 0.75 0.80 0.61 0.70 0.79 0.64 0.73 0.82 0.57 0.63 0.69

St Dev of Queuing Time 0.26 0.32 0.37 0.14 0.21 0.27 0.14 0.18 0.23 0.11 0.14 0.17

% Queued less than time limit 96.44 96.56 96.68 98.25 98.36 98.48 98.58 98.67 98.77 98.80 98.89 98.97

Utilization % 37.60 37.76 37.91 33.03 33.15 33.28 29.43 29.55 29.67 31.84 31.97 32.09

10am-2pm 100% volume 5-2-3-2 5-2-4-2 6-2-2-2 6-2-3-2




Items Entered 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45



Time 0.42 0.50 0.59 0.44 0.52 0.61 0.44 0.49 0.54 0.31 0.38 0.44



81

Utilization % 28.52 28.62 28.73 25.79 25.88 25.98 27.61 27.73 27.84 25.07 25.17 25.27

2pm-7pm 100% volume 4-2-2-2 4-2-2-3

Performance Measure -99% Average 99% -99% Average 99%


Maximum Queuing Time 1.96 2.85 3.74 0.61 1.07 1.53

Items Entered 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45

Average Queuing Time 0.00 0.00 0.00 0.00 0.00 0.00


Time 0.37 0.44 0.51 0.23 0.33 0.43


% Queued less than time limit 99.83 99.86 99.89 99.98 99.99 99.99

Utilization % 26.85 26.96 27.07 23.50 23.59 23.67

7pm-12am 100% volume 4-2-2-2 4-3-2-2 4-4-2-2 4-2-2-3




Items Entered 35812.71 35856.10 35899.49 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45



Time 3.01 3.12 3.23 1.10 1.16 1.22 0.92 1.01 1.10 1.15 1.21 1.27



Utilization % 36.77 36.89 37.00 30.77 30.89 31.00 27.05 27.16 27.27 31.62 31.75 31.87

2am-2:30am 100% volume 4-2-2-2 4-3-2-2 4-4-2-2




Items Entered 35742.69 35842.70 35942.71 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45


Average (non-zero) Queuing Time 3880.33 4136.04 4391.75 71.33 74.15 76.96 71.33 74.15 76.96



Utilization % 99.72 99.85 99.98 84.70 85.03 85.36 84.70 85.03 85.36

82

2am-2:30am 100% volume 4-5-2-2 4-6-2-2 4-7-2-2


Maximum queue size 26.46164 32 37.53836 8.01019 9.9 11.78981 8.01019 9.9 11.78981


Items Entered 35812.451 35870 35927.549 35811.449 35869.45 35927.451 35811.449 35869.45 35927.451



Time 1.99839 2.23266 2.46693 0.7433 0.80059 0.85788 0.7433 0.80059 0.85788



Utilization % 56.37336 56.59478 56.81619 42.30602 42.4679 42.62977 42.30575 42.46772 42.62969

12am-2am 115% volume 4-2-2-2 4-3-2-2 4-4-2-2




Items Entered 41167.65 41230.25 41292.852 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98





Utilization % 55.52 55.74 55.95714 47.13 47.32 47.51 37.91 38.07 38.23

2am-7am 115% volume 4-2-2-2 4-3-2-2 4-4-2-2




Items Entered 41182.13 41226.23 41270.34 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98




83


Utilization % 99.89 99.93 99.98 81.05 81.38 81.71 60.72 60.97 61.21

2am-7am 115% volume 4-5-2-2 4-6-2-2 4-7-2-2




Items Entered 41171.02 41232.00 41292.98 41167.65 41230.25 41292.85 41171.02 41232.00 41292.98





Utilization % 48.57 48.77 48.97 40.48 40.64 40.79 34.70 34.84 34.99

7am-10am 115% volume 4-4-2-2 4-4-2-2 4-4-2-2 4-4-2-2




Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98



Time 1.19 1.27 1.35 0.71 0.75 0.80 5.78 6.12 6.46 206.47 230.74 255.02



Utilization % 31.10 31.22 31.34 37.91 38.07 38.23 60.72 60.97 61.21 97.29 97.65 98.00

84

10am-2pm 115% volume 4-2-2-2 4-2-3-2 4-2-4-2 5-2-2-2




Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98



Time 5.17 5.43 5.69 0.71 0.78 0.85 0.75 0.82 0.89 5.17 5.43 5.69



Utilization % 58.26 58.48 58.71 37.92 38.08 38.23 33.79 33.93 34.08 58.26 58.48 58.71

10am-2pm 115% volume 5-2-3-2 5-2-4-2 6-2-2-2 6-2-3-2




Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98



Time 0.66 0.71 0.76 0.48 0.53 0.58 0.45 0.48 0.52 0.34 0.38 0.43



Utilization % 36.58 36.74 36.90 29.62 29.74 29.86 31.72 31.85 31.98 28.78 28.90 29.03

2pm-7pm 115% volume 4-2-2-2 4-2-2-3 4-2-2-4




Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98



85



Utilization % 30.86 30.98 31.11 27.00 27.11 27.21 24.44 24.54 24.63

2pm-7pm 115% volume 4-2-3-2 4-2-3-3 4-2-3-4




Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98





Utilization % 27.17 27.28 27.39 24.14 24.23 24.33 22.08 22.17 22.26

7pm-12am 115% volume 4-2-2-2 4-3-2-2 4-4-2-2




Items Entered 41184.45 41230.25 41276.05 41187.39 41232.00 41276.61 41187.39 41232.00 41276.61



Time 3.88 4.01 4.14 1.41 1.47 1.53 1.22 1.27 1.33



Utilization % 42.27 42.39 42.51 35.38 35.48 35.58 31.13 31.22 31.31

2am-2:30am 115% volume 4-2-2-2 4-3-2-2 4-4-2-2




Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98



86



Utilization % 99.87 99.92 99.98 97.29 97.65 98.00 97.29 97.65 98.00

2am-2:30am 115% volume 4-5-2-2 4-6-2-2 4-7-2-2




Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98



Time 4.33 4.99 5.65 0.88 0.94 1.00 0.88 0.94 1.00



Utilization % 64.75 65.02 65.29 48.57 48.77 48.96 48.57 48.77 48.96

87

100% volume 4-2-2-2 5-2-2-2 6-2-2-2 7-2-2-2




Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49



Time 4.74 5.11 5.48 5.78 6.26 6.74 6.64 7.27 7.90 7.10 7.60 8.10



Utilization % 41.85 41.98 42.11 38.05 38.17 38.29 34.88 34.99 35.10 32.20 32.29 32.39

100% volume 4-2-2-2 4-3-2-2 4-4-2-2




Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49



Time 4.74 5.11 5.48 1.56 1.66 1.75 1.49 1.55 1.60



Utilization % 41.85 41.98 42.11 38.02 38.14 38.25 34.81 34.92 35.03

100% volume 5-2-2-2 5-3-2-2 5-4-2-2




Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49



Time 5.78 6.26 6.74 1.18 1.36 1.54 0.97 1.04 1.11



Section 2: Results from 24 Hour Analysis

88

Utilization % 38.05 38.17 38.29 34.84 34.96 35.07 32.15 32.24 32.34

100% volume 6-2-2-2 6-3-2-2 6-4-2-2




Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49





Utilization % 34.88 34.99 35.10 32.18 32.28 32.38 29.84 29.94 30.04

100% volume 4-2-2-2 4-2-3-2 4-2-4-2




Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49



Time 4.74 5.11 5.48 5.19 5.58 5.96 5.35 5.73 6.12



Utilization % 41.85 41.98 42.11 38.07 38.19 38.31 34.93 35.03 35.13

100% volume 4-2-2-2 4-2-2-3 4-2-2-4




Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49





89

Utilization % 41.85 41.98 42.11 38.08 38.19 38.31 34.88 34.99 35.10

100% volume 5-2-2-2 5-2-2-3 5-2-2-4




Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49





Utilization % 38.05 38.17 38.29 34.88 34.99 35.11 32.21 32.31 32.41

115% volume 4-2-2-2 5-2-2-2 6-2-2-2 7-2-2-2




Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34


Average (non-zero) Queuing Time 6.05 6.42 6.79 7.28 7.79 8.30 8.78 9.44 10.11 9.45 10.09 10.74



Utilization % 48.10 48.25 48.40 43.73 43.87 44.00 40.09 40.21 40.33 37.00 37.12 37.24

115% volume 4-2-2-2 4-3-2-2 4-4-2-2




Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34





90

Utilization % 48.10 48.25 48.40 43.69 43.83 43.96 40.00 40.12 40.25

115% volume 5-2-2-2 5-3-2-2 5-4-2-2




Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34



Time 7.28 7.79 8.30 1.64 1.80 1.97 1.15 1.23 1.31



Utilization % 43.73 43.87 44.00 40.05 40.17 40.29 36.93 37.04 37.16

115% volume 6-2-2-2 6-3-2-2 6-4-2-2




Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34



Time 8.78 9.44 10.11 1.77 2.02 2.27 1.09 1.20 1.31



Utilization % 40.09 40.21 40.33 36.96 37.08 37.20 34.31 34.41 34.51

115% volume 4-2-2-2 4-2-3-2 4-2-4-2




Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34





91

Utilization % 48.10 48.25 48.40 43.76 43.89 44.03 40.14 40.27 40.40

115% volume 4-2-2-2 4-2-2-3 4-2-2-4




Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34





Utilization % 48.10 48.25 48.40 43.74 43.88 44.02 40.11 40.23 40.35

115% volume 5-2-2-2 5-2-2-3 5-2-2-4




Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34





Utilization % 43.73 43.87 44.00 40.07 40.20 40.33 37.01 37.12 37.23

92

Appendix B: User Manual for SIMUL8 Simulation Model

The SIMUL8 simulation model was constructed to imitate the occurrences of

the system over time, in an attempt to infer possible improvements in call taking

functionality. This appendix gives a brief description of the model, and several

instructions on how to operate and modify the model.

Purpose

The purpose of the simulation model was to determine a minimal workforce

level for the call taking functionality, subject to a pre-determined service goal. This

was achieved by constructing a virtual imitation of the physical system, endowing the

simulation with real world parameters and data, and performing numerous trials with

variable workforce levels, to determine the percentage of calls processed within a

given service level. While several trials were run over a 24 hour period, the user is

also able to manipulate the analysis to focus on specific time windows in order to

address certain problem periods, if necessary.

93

Step 1: Using the Supplementary Excel File

The supplementary Excel file is a program that takes a given shift

combination, which will state the number of workers assigned per shift, and breaks

down the worker availability into 15 minute intervals. This is required as the

simulation model specifies the workforce level availability every 15 minutes.

Upon opening the supplementary Excel file, go to the sheet titled “Call Takers

per Shift”. Enter the required shift combination into the yellowed cells: Cell C14:F14.

Then, proceed to sheet “Shift Export” and copy the numbers within the bolded box,

which are represented by Cells B4:B99.

Step 2: Update the Simulation Model with Altered Shift Pattern

Upon opening the Simul8 file, access the “Information Store” function,

located under the tab “Objects”; this can also be accessed by pressing the following

keys: Ctrl-I. Under the “Spreadsheet” objects, open the spreadsheet “Shift Patterns”

by selecting the file and choosing the options “Properties” in the vertical menu option

in “Information Store”. Upon opening the spreadsheet “Shift Patterns”, select the

option “View” in the vertical menu option; this will result in the Excel sheet being

opened. Select the “Edit Formats” option in the vertical menu option, indicated

below, and open the Formula One Workbook; opening the Formula One Workbook

allows for pasting large values or subsets of data into the spreadsheet. Paste the

copied shift pattern into the Excel workbook. Close the file, and select “Ok” for all

preceding applications still open.

94

Step 3: Run Simulation Model

Ensure the clock is reset; run the simulation model by selecting the “Run”

button on the main menu.

Edit Formats

“Run” button

Figure 23: Image of Simul8 Toolbar

Figure 22: Image of Simul8 Information Store – Spreadsheet for

Staffing Levels

95

Additional Applications

1. Changing Simulation Duration

Select the option “Clock” in the main menu bar. Select the option “Go to

Simulation Time” and enter the appropriate duration.

2. Changing Clock Properties

Select the option “Clock” in the main menu bar. Select the option “Clock

Properties”. Within this option, the time unit, the associated days, as well as

hour of the days analyzed (time windows), can be specified. The appearance

of the clock can also be altered within this option.

3. Accessing the Results Summary

Select the option “Results” in the main menu bar. Select the option “Results

Summary”.

4. Adding Article Variables to the Results Summary

Open the desired article (for example: work centre, resource, queue etc.).

Open the “Results” option and right click the desired variable.

5. Conduct Trials

To conduct trials instead of a single run, select the option “Trials” in the main

menu bar. Enter the number of trials required, the necessary Base Random

Number Set, and the Name of the trial. Visual display of results can also be

modified by options available within this functionality. To start the trial, select

the option “Run trial”.

96

6. Adding Another Work Centre

Physically Add Another Work Centre

To physically add another work centre, select and copy any current work

centre; this can typically be performed by pressing the following keys:

Ctrl-C. Paste the new work centre and connect to the main diagram with

flow arrows. Flow arrows should be connected from the queue “Queue for

Calls” to the new work centre, and then from the work centre to the

“Completed Calls” Finished Node. It is necessary to copy and paste a new

work centre to ensure that all visual logic code is also perpetuated to the

new work centre created.

Update the Visual Logic/Information Store for the queue “Queue for Calls”

The visual logic that references the number of work centres within the

simulation model was built with a variable that is located in the

“Information Store”. The total number of work centres must be updated

for the visual logic code to be viable. Therefore, the only required step to

update the total number of work centres is an update of this variable. To

access the variable, select the option “Objects” and select the option

“Information Store”. Under the heading of “Numbers”, select the object

“num_wc” and update the “Contents” to the variable amount.

97

Appendix C: User Manual for Excel-based Call Taker Model

An Excel-based model was constructed in order to validate the results found

in Simul8. This appendix describes the model and how to use it in Excel.

Purpose

The purpose of the Excel-based model is to allow a user to manipulate a

number of variables that affect call volume, and based on those variables, the model

calculates the minimum required number of call takers to meet that volume.

Presentation of Results

The output of the model, which is the minimum number of call takers, comes

in two forms, numerical and graphical. The numerical form is found in the sheet “Min

Call Takers” in columns M and AI. The graphical form is found in the sheet “Weekly

Graph” and shows, for each hour of the week, a bar graph with the minimum number

of call takers.

Two ways of modeling the information are available. One method assumes an

average call duration that combines all call types into one. It is represented in “Min

Call Takers” in columns I through M and in “Weekly Graph” in Figure 1. The second

way assumes three distinct call types, emergency, non-emergency, and

administrative. Each has its own distinct characteristics. This method is represented in

columns S to AI in “Min Call Takers” and in Figure 2 in “Weekly Graph”. Although

both methods produce fairly similar results, the second method is believed to be more

accurate since it creates a better representation of reality.

98

Description of the Model

The top left corner of the sheet “Min Call Takers” can be considered as the home

screen for this model. The cells coloured in bright green are variables that may be

changed. Many cells have a small red triangle in the upper right corner; these indicate

that comments are available for this cell. By placing the mouse on top of the cell,

comments will become visible in a nearby yellow box. Most of these boxes either

give instructions on how to manipulate that cell, or in the case where the cell is not

manipulable, it says what the value means.

Below are some definitions of the cells in yellow whose titles correspond to

manipulable values for the cells in green.

Desired Busy Rate: the fraction of time that, on average, call takers will be on phone

answering calls. For example, a 100% busy rate implies that the call taker never

hangs up their phone.

Availability Rate: the inverse of the busy rate, this value is the fraction of time that

call takers will be idle and thus available to answer any incoming calls. This value is

a function of the desired busy rate and will change automatically when the busy rate

is changed.

Probability: from a given Erlang distribution, this number represents the percentile

from which the number of calls arriving in one hour will be used. For example,

Figure 24 below shows the call distribution for Monday from 8am-9am. The Erlang

distribution which best fits the data has parameters alpha = 9 and beta = 3.4346. The

90th percentile, which is represented by the red bar at the bottom, happens to be 44.63

99

calls per hour. If the probability value was changed to 0.5, the 50th percentile would

be used, which (not shown in the figure below) is 29.77 calls per hour.

Figure 24: Example of Erlang distribution for calls on Monday from 8am-9am

Total Call Volume and Hourly Call Changes: These cells represent, in effect, a

“switch” between two possible modes that the model has. Only one mode can be

turned on at a time. A mode is turned on by typing “1” in the green cell next to it, and

“0” in other mode’s green cell. If both cells are “1”, a red error message will appear.

The Total Call Volume mode allows the user to change the average call

volume for every hour of the week at once. The default is set to 100%, which is

approximately the average of 36,000 calls per month. By changing the value to, for

example, 115%, it means that a 15% increase in call volume will occur everywhere

(that is, for every hour of the week).

100

The Hourly Call Changes is the second mode, and it allows the user to

manually manipulate call volume for any hour(s) of the week. When this mode is

turned on, the user can go to the sheet “Weekly Graph” and scroll the right, where

there is a group of cells for every hour of the week. Any of the values can be changed,

and the effect of that change can immediately be seen in the graphs to the left

(description of the graphs are below). For example, to simulate a large accident on a

Saturday afternoon that increased call volume by 50%, the value of “150%” could be

typed into the chart for Saturday for the hours of 3pm, 4pm and 5pm. The resulting

effect – an increase in the required number of call takers – will be immediately seen

in the graphs to the left.

It should be noted that when using this mode to simulate such a situation, the

busy rate should be increased, say, to 95%, otherwise the model will calculate the

number of call takers required for an increased number of calls, while still assuming a

65% busy rate.

Simulation Modeling for Staff Optimization of the Toronto ... · PDF fileSimulation Modeling for Staff Optimization of the Toronto Emergency Medical Services Call Centre ... USER MANUAL

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