Mohd Queueing 1999

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QUEUEING SIMULATION USING EXCEL 2000

A Mini-Study Project presented to the Graduate School of

Business of the University of Stellenbosch in partial

fulfilment of the requirements for the degree of

Masters Degree in Business Administration (MBA)

by

Shivan Mohd

Study Leader : Professor WR Gevers

Degree of Confidentiality : Grade A

Date : October 1999


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DECLARATION

Hereby I, Shivan Chad Mohd, declare that this study project is my own original work and that all

sources have been accurately reported and acknowledged, and that this document has not been

previously in its entirety or in part been submitted at any university in order to obtain an

academic qualification.

S. C. Mohd 4 October 1999

Stellenbosch University http://scholar.sun.ac.za


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ACKNOWLEDGMENTS

The author wishes to express sincere appreciation to Prof WR Gevers for his assistance in the

preparation of this manuscript. In addition, I would like to thank SPL for allowing me to make

use to their computer and printing equipment and making time available for me to complete

this mini-study project.

The core of this project is a computer simulation model. Although every effort has been taken to

ensure the proper operation of the model, neither the author of the program, nor the study leader

can and will be held liable for any loss of income due to incorrect information used in the

program. The program must be used as aid in making a business decision and not the deciding

factor. At the time of release, the software had no form of virus attached to it. For a more

definitive solution, the author could be contacted and will give guidelines as to your specific

problem.



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ABSTRACT

A mini-study project presented on the use of Microsoft Excel 2000 in the field of simulation.

The mini-study project covers the principles of queuing and it’s outputs. The simulation model

will test various scenario’s of queuing theory. Inputs can be changed to suit the users

requirements. Results may be analysed to determine an optimal queuing environment.



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OPSOMMING

Hierdie mini-werkstuk illustreer die gebruik van Excel 2000 in die veld van simulasie. Die

beginsels van toustaan modelle word gedek, asook die tipiese resultate. Die simulasiemodel

modelleer en toets verskillende toustaan scenarios. Toevoere kan verander word na gelang van

die gebruiker se keuse. Die resultate kan ontleed word om die optimale toustaan omgewing te

bepaal.



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TABLE OF CONTENTS

Declaration ii

Acknowledgments iii

Abstract iv

Opsomming v

List of tables viiiList of figures ix

CHAPTER 1. INTRODUCTION 1

1.1 INTRODUCTION 1

1.2 METHODOLOGY USED 2

1.3 LIMITATIONS AND RESTRICTIONS 2

1.4 MINIMUM REQUIREMENTS 3

1.5 DEVELOPMENT OF THE REPORT 3

CHAPTER 2. QUEUING THEORY: A QUICK OVERVIEW 4

2.1 INTRODUCTION 42.2 THE STRUCTURE OF THE QUEUING SYSTEM 4

2.2.1 The Customers and their source 4

2.2.2 The arrival process 4

2.2.3 The service facility and service process 5

2.2.4 The Queue 5

2.2.5 Degree of Patience 6

2.3 SUMMARY 6

CHAPTER 3. THE LOGIC OF THE MODEL PRESENTED 7

3.1 INTRODUCTION 73.2 INPUTS REQUIRED 7

3.2.1 Unit of time 7

3.2.2 The duration of the simulation 7

3.2.3 The number of servers 7

3.2.4 The maximum number of customers allowed in the queue 8

3.2.5 The arrival rate 8

3.2.6 The service rate 9

3.3 SIMULATION OF RANDOM EVENTS 9

3.3.1 Exponential 9

3.3.2 Constant 9

3.3.3 Normal 103.3.4 Triangular 10

3.3.5 Observed Probabilities 10

3.4 SEQUENCE OF EVENTS 11

3.5 SUMMARY 12

CHAPTER 4. VERIFICATION OF MODEL 13

4.1 INTRODUCTION 13

4.2 ANALYTICAL MODELS 13

4.3 SIMULATION RESULTS 14

4.4 OTHER STEPS TO VALIDATE RESULTS 15

4.5 SUMMARY 17



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CHAPTER 5. USER GUIDE 18

5.1 INTRODUCTION 18

5.2 USING THIS GUIDE 18

5.3 CONTROL CENTRE 19

5.4 ACTIONS BUTTONS 21

5.4.1 “Change Inputs” Button 21

5.4.2 “Run Simulation Button” Button 24

5.4.3 “Add to History File” button 26

5.4.4 “Clear History” Button 26

5.5 NAVIGATION BUTTONS 26

5.6 SUMMARY 28

CHAPTER 6. SUMMARY AND RECOMMENDATIONS 29

6.1 SUMMARY 29

6.2 RECOMMENDATIONS 29

LIST OF SOURCES 30

APPENDIX A :LIST OF ROUTINES AND THIER FUNCTIONS 31

APPENDIX B: LIST OF SCREENS 33

APPENDIX C: VISUAL BASIC CODE 43



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LIST OF TABLES

Table 2.1: Examples of queues 6

Table 3.1: Sequence of events 11

Table 4.1: Inputs for comparison 14

Table 4.2: Comparison of results 14

Table 4.3: A sample of the details table 15

Table 4.4: Input time versus simulated time 16

Table 4.5: Statistical comparison 16



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LIST OF FIGURES

Figure 5.1: Welcome Screen 19

Figure 5.2: Control Centre 20

Figure 5.3: Input Screen 21

Figure 5.4: Inter-arrival Input Box 23

Figure 5.5: Service Inputs 24

Figure 5.6: Probability Table 25

Figure 5.7: History Screen 26

.



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CHAPTER 1

1. INTRODUCTION

1.1 INTRODUCTION

Queuing is a part of many people’s lives. Managing queues and keeping them as short as

possible is a mammoth task and many people prefer to avoid the exercise of trying to calculate

the most user friendly and cost effective queuing environment. In an attempt to make this task a

bit easier, the model developed, will show the characteristics of queues by simulating the

queuing environment.

The model was designed and created for two main reasons:

To simulate a queuing environment based on various factors of queuing e.g. arrival

distribution, services rate, number of servers etc and presenting the results in format that

would make the analysis of the results easier.

The second reason is to show students:

a) how problems (in this case: queuing), can be solved by using spreadsheets as the analytical

tool and by allowing the student to try various combinations of inputs and comparing results;

b) the logic of queuing simulation.

Students and managers who wish to optimise the operations where people or items needs to be

serviced within an appropriate time could use the model. The Model will report simulated results

of the users inputs, thus allowing for various scenarios. Optimal loading for service points could

be determined. It would also allow for controlling queue length and server idle time. In most

situations, a simulation model is a computer model that imitates a real-life situation. Often,

simulation can provide the decision maker with important information. A simulation model

might help answer questions such as the following:

If a service point is added, how will the average waiting time of the customer decrease?



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If the service time is reduced, by how much will the average waiting time reduce?

Although analytical models can help in answering the questions above, simulation will give the

user a better feel as to the possible outputs of the data inputted. The program caters for both

theoretical probability distributions and observed probabilities.

1.2 METHODOLOGY USED

The model was created using Excel 2000. The main objectives are, to show how simulation can

be accomplished by using Excel spreadsheets and for the model to be practical in application.

Most of the program logic uses Visual Basic and Excel functions to simulate data and calculate

results. Once the program was complete, the data produced were validated using random checks

and the use of an analytical model to compare the analytical results against simulated results. By

covering the theory of queuing, the user will have a better understanding of the model. The

limitations of the model will be discussed in the next paragraph.

1.3 LIMITATIONS AND RESTRICTIONS

The program has its limitations and should only be used as a guideline. It makes the following

assumptions:

The population is from an infinite source

Customers arrive individually and not in groups

Only single or multi-facility – No mixed facility

First come first served

The model does not take into account the following:

Balking

Reneging

Costs



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1.4 MINIMUM REQUIREMENTS

For the model to work, the following minimum requirements with respect to hardware and

software must be adhered to:

486 100 MHz processor

At least 26 MBytes of RAM

Excel 97 or higher

Windows 95 or higher

1.5 DEVELOPMENT OF THE REPORT

The report covers the following subject areas:

Queuing theory: a quick overview – A revision of queuing theory and the area the model will

cover, is presented. The queuing theory chapter will help the user in recapping on the theory

of queuing which would help the user understand the logic and results produced.

Logic of the model presented – Understanding how the results were derived is a key factor

when working with the model presented. The sequence of the simulation is covered in this

area.

Verification of the model – The focus of this chapter is to prove that the results are correct.

The user may be more comfortable in using the model once it has been proven that the model

produces the correct results.

User guide – If a user requires clarification as to how the program is to be used, a section

covering the use of the program is included in this document.



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CHAPTER 2

2. QUEUING THEORY: A QUICK OVERVIEW

2.1 INTRODUCTION

In order to understand the program, an overview to discuss some important points and

terminology would be appropriate and helpful when working through the program. The chapter

covers the minimal requirements needed for the simulation of queues.

2.2 THE STRUCTURE OF THE QUEUING SYSTEM

2.2.1 The customers and their source

Customers are defined as those in need of service. Customers can be people, aeroplanes,

machines or raw materials. The customers are generated from a population (calling population)

or a source. The population source may be from an infinite or a finite source. For example, a

hospital’s population would be residents in the surrounding community and the customers would

be those sick people in the population requiring hospitalisation.

2.2.2 The arrival process

The manner in which customers show up at the service facility is called the arrival process. The

distributions of the inter-arrival time may be exponential, constant etc. The average service time

per server is different from the average inter-arrival time, as the two processes are independent

of each other. When describing a waiting system, the manner in which customers or the waiting

units, are arranged for service, must be defined. Waiting line formulas generally require an

arrival rate, or the number of units per period (such as 10 units per hour). The time between

arrivals is the inter-arrival time (such as an average of one every six minutes) or, the reciprocal

of the arrival rate.



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A constant arrival distribution is periodic, with exactly the same time between successive

arrivals. In productive systems, about the only arrivals that truly approach a constant inter-

arrival period are those that are subject to machine control. Much more common are variable

(random) arrival distributions. In observing arrivals at a service facility, there are two

viewpoints: The time between successive arrivals can be analysed to see if the times follow

some statistical distribution. Usually, in elementary analytical models it is assumed that the

time between arrivals is exponentially distributed.

2.2.3 The service facility and service process

The service is provided by a service facility (or facilities). The service facility may be a person

(bank teller, a barber, machine (elevator, gasoline pump), or space (airport runway, parking lot,

hospital bed), to mention just a few. A service facility may include one person or several people

operating as a team.

Facilities may be fixed (Loading dock) or movable (service technician). The service time may

also follow various distribution patterns, exponential etc.

In elementary models, the exponential distribution is assumed.

2.2.4 The Queue

Whenever an arriving customer finds that the service facility is busy, a queue or waiting line is

formed. Examples of Systems, Queues formed and the Service provided may be found in Table

2.1.



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Table 2.1: Examples of queues

System Queue Service

Computer Jobs Process facilities

Bank People Tellers

Telephone Callers Switchboards

Library Books to be shelved Librarian’s Assistants

2.2.5 Degree of patience

A patient client is one who waits as long as necessary until the service facility is ready to serve

him or her. (Even if clients grumble and behave impatiently, the fact that the customers wait is

sufficient to label them as patient clients for purposes of waiting line theory.)

There are two classes of impatient clients. Members of the first class arrive, survey both the

service facility and the length of the line, and then decide to leave. Those in the second class

arrive, view the situation, join the waiting line, and then, after some period of time, depart.

The behaviour of the first type is termed balking, while the second is termed reneging.

The program does not cater for impatient behaviour.

2.3 SUMMARY

The understanding of queuing theory is fundamental, when trying to apply the concepts to

simulate an environment. Understanding waiting lines or queues and learning how to manage it,

is one of the most important areas in operations management. Simulation will aid management

in this understanding. It is basic to creating schedules, job design, inventory models and so on. In

a service economy people wait in line every day, from driving to work to checking out at the

supermarket. Management can reduce the amount of time spent in a queue by applying the

concepts of queuing theory.



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CHAPTER 3

3. THE LOGIC OF THE MODEL PRESENTED

3.1 INTRODUCTION

Once a good understanding of the queuing theory has been formed, the user will have a better

understanding of the logic of the model presented. The purpose of this chapter is to clarify the

flow of inputs, processes and outputs of the model.

3.2 INPUTS REQUIRED

3.2.1 Unit of time

The unit of time may be Minutes, Hours or Days. Once the user uses either one of these options,

the program will use that unit of time for both the arrival and the service calculations.

3.2.2 The duration of the simulation

The duration of the simulation pertains to the length of time the simulation should run. For

example: 25 will equal 25 Days if the Unit of time is days. The longer it is set the longer the

simulation will take to run. Normally a longer run will give an answer closer to that of the

analytical models. If, for example, the simulation run time is set for 10 min and the arrival rate is

one per minute, the program will return approximately 10 observations.

3.2.3 The number of servers

The number of servers that are used or that will be used is required. The option allows the user

to change from a single server environment to a multi-server environment with all servers

rendering an identical service.



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3.2.4 The maximum number of customers allowed in the queue

The user can set the number of customers the queue can handle. For example: 20 will mean that

once the queue length reaches 20, customers would be turned away until the number in queue

drops to below 20. The customer who will be turned away will then be recorded under the

“Number of Customers turned away” heading on the report sheet. The parameter is governed by

the size available for queuing. If the area in which people are allowed to queue can only house

10 people then the limit must be set to ten. If unlimited space is available for queuing then the

parameter must be set to 1000.

3.2.5 The arrival rate

The average arrival rate will be in the form of e.g. seven per time of unit. It means that if the

customers arrive at a rate of 7 every hour (time unit) then the inter-arrival time will be 1/7 =

0.143 hours between arrivals, and this is the number placed in the input box. The average inter-

arrival time is automatically converted to an arrival rate, which is reported to the Input Screen.

The inter-arrival time on the Input Screen will not be used if the program is using the observed

probability option. By using the Monte-Carlo methodology, random times will be selected from

the inter-arrival probabilities table. The inter-arrival time is then used in the simulation process.

The distribution pattern of the inter-arrival times may be:

Exponential

Constant

Normal

Triangular

Or Observed probabilities



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3.2.6 The service rate

The average service rate will be in the form of e.g. six per time of unit. It means that if the

customers arrive at a rate of 6 every hour (time unit) then the average time per service will be 1/6

= 0.166 hours, and this is the number placed in the input box. The average time per service is

automatically converted to a service rate, which is reported to the Input Screen. The average time

per service on the Input Screen will not be used if the program is using the observed probability

option. By using the Monte-Carlo methodology, random times will be selected from the service

time probabilities table. The average time per service is then used in the simulation process

The distribution pattern of the mean service time is independent of that of the inter-arrival

times.

3.3 SIMULATION OF RANDOM EVENTS

When simulating data, random numbers are required. In the model, random numbers are

required for the inter-arrival time and the service time. Excel provides a facility that generates

random numbers. In the Visual basic format, the “Rnd” function is used. When observed values

are used, the Monte Carlo methodology is used to generate random times.

Five different probability distributions may be selected. Duration’s are simulated as shown

below for the various distributions.

a) Exponential

When the exponential option is selected, the program uses the following statement:

Duration = MeanArriveTime * Log(Rnd)

Where “Log” represents the natural logarithm.

b) Constant

When the constant option is selected, the program uses the following statement:



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Duration = MeanArriveTime

c) Normal

When the normal option is selected, the program uses the following statement:

Duration = NormInv (Random Number, Standard Deviation, MeanArriveTime) (Returns the

inverse of the normal cumulative distribution for the specified mean and standard deviation)

If a negative number is generated, the program will loop until the generated number is positive.

Only positive numbers are used in the simulation.

d) Triangular

When the triangular option is selected, the program uses the following statement:

ValA = (MaximumValue - MinimumValue)

If Randomnum


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For example, an inter-arrival time of six may have a probability of 20%. Of all the other inter-

arrival times the inter-arrival time of six appears 20% of the time within the given environment.

The formulae used within Excel to determine the times based on the probabilities: =

VLOOKUP().

The duration is calculated by generating a random number e.g. 0.54 and using it as a percentage.

The random number is used to compare the number against the probability table generated by

the user. The comparison will result in a corresponding inter-arrival or service time. The

newfound time is used as the duration within the simulation program.

3.4 SEQUENCE OF EVENTS

To start the simulation the user has to click on the Run Simulation button. Once this has been

done, the following sequence of events takes place:

Table 3.1: Sequence of events

Main Routine Description of what it does Sub Routine Description of what it does

RunSimulation Gathers the users input parameters from

the Inputs worksheet. Starts the Initialize Routine

Initialize Re sets the simulation parameters to Zero.

Sets the worksheet parameters to Zero

Calculates the First Arrival based on the users inpute.g. Exponential, Normal etc

RunSimulation Start a loop until the simulation time hasexpired as per the users input.

Starts the Timing Routine

Timing Determine whether the time is an arrival or adeparture event.

Update the Clock to the time of the next event

RunSimulation Start the UnpdateAreas Routine

UpdateAreas Update statistical accumulators and writes results tothe reports worksheet

RunSimulation Check to see if this time is an arrivalevent or a departure event.

If it is an arrival event then run the ArriveRoutine

Starts the Arrive Routine

Arrive Checks the input sheet for which distribution patternto use

Once found, it calculates the random time of the nextevent

Check to see if the number in queue is within themaximum allowed in the queue. If above the amountof customers allowed then the programme recordsthe arrival as a lost customer.

Check if all servers are busy, and if so, put the timeat the end of the queue. If not, then put thecustomers directly into service.

Before it can place a customer in service, it searchesfor the first available server by starting from servernumber one and progressing upwards towards thelast server.

Once in service it now calculates a random servicetime

Write the information to the detailed report sheet.

RunSimulation If the Event was a departure event then



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run the depart routine.

Depart Update the number of customers who finished

Check if any customers are in queue, if not, thenmake the server available else take the customerinto service

If taken into service, schedule a departure for thecustomer, based on the chosen service distributionpattern.

Move everyone else up in the queue.

RunSimulation Loop until the simulation reaches theend of the time stipulated.

Run the Check Routine

Check Fills any blanks with zeros within the worksheets.

RunSimulation Run the finishoff Routine

Finishoff Format the sheets to make it look presentable

RunSimulation Run the Averages Routine

Averages Based on the previously generated information theaverage times are calculated and presented in formof a summary

RunSimulation Run the Queuelength Routine

Queuelength Calculates the number of customers waiting in lineat a particular point in time.

RunSimulation Run the Buildreport Routine

Buildreport Copies the details sheet

Renames the copy

Adds data from other sheets Format the copy into a presentable format

RunSimulation Run the Report Routine

Report Builds the report sheet

RunSimulation Run the CreateChart Routine

CreateChart Creates a chart based on the percentages reportedin the report sheet

RunSimulation Select the Reports worksheet

Close the Control panel dialog box.

A comprehensive list of all the routines and what functions it performs can be found in

Appendix A. Appendix C shows the actual code used to generate the results.

3.5 SUMMARY

The fundamental aim of the chapter is to show the user how the results are generated on a logical

level and the emphasis was removed from the more technical programming side. Many

computations are made to get a result before the next routine may execute, but once the logic is

set-up correctly, the results will be consistent. Users may find the visual basic code to be lengthy

and complex, however Excel still performs at a reasonably fast pace.



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CHAPTER 4

4. VERIFICATION OF MODEL

4.1 INTRODUCTION

The purpose of the verification stages is two fold:

To prove that the results are reliable and the model works correctly.

To ensure that the results are consistent and accurate. The word accurate is used loosely as in

simulation, the result will vary every time but should average out closely to the analytical

results.

The methodology used will be:

Show which formulas will be used to test the results.

Build a table of inputs (Table 4.1), which will include both single and multiple servers.

Insert the input data in to the analytical formulas.

Insert the input data into the simulation model.

Compare the average simulated results to the analytical result (Table 4.2). (Outputs)

Compare theoretical inter-arrival times to simulated inter-arrival times (Table 4.4). (Input)

Compare theoretical service times to simulated service times (Table 4.4). (Input)

Compare theoretical statistical data to simulated statistical data (Table 4.5).

4.2 ANALYTICAL MODELS

An analytical model, which was supplied by Professor WR Gevers, was used to test the results

of the simulated model.

The model properties are based on the:

M / M / s model.



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In the above model M / M denotes that both the inter-arrival times and the service time for each

server is exponentially distributed. “s” denotes the number of servers. Customers are serviced in

a First-Come-First-Serve fashion.

4.3 SIMULATION RESULTS

Five different models based on the exponential distribution were analysed. The input parameters

are shown in Table 4.1. The analytical results together with the results of each of three

simulation runs are reported in Table 4.2.

Table 4.1: Inputs for comparison

Inputs Run1 Run2 Run3 Run4 Run5

Average Inter-arr ival t ime 0.04 2.00 0.40 0.17 0.27

Average Service time per

server

0.03 1.50 2.00 0.60 0.50

Number of servers 1 1 6 3 2

Traff ic intensity 0.75 0.75 0.83 1.18 0.93

Units Days Minutes Minutes Days Hours

Durat ion of run 500 800 800 500 1000

Table 4.2: Comparison of results

Outputs Run1 Run2 Run3 Run4 Run5

Average Time in Queue

Analyt ical 0.090 4.500 1.290 Traffic 2.977

Simulated Run 1 0.095 4.196 1.090 intensity 2.765

Simulated Run 2 0.093 4.375 1.440 To high 2.673

Simulated Run 3 0.089 5.689 1.200 3.000

Units Days Minutes Minutes Days Hours

Average Number in Queue

Analyt ical 2.250 2.250 3.230 Traffic 11.024

Simulated Run 1 2.405 2.080 2.843 intensity 10.230

Simulated Run 2 2.307 2.010 3.521 To high 9.856

Simulated Run 3 2.238 2.860 3.345 11.277



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The simulated results appear to be similar to the analytical results. When running the program it

was found that the higher the traffic intensity the longer the simulation should run to get a

simulated answer similar to the analytical answer. The comparison above, focus’s on the output

data.

4.4 OTHER STEPS TO VALIDATE RESULTS

Table 4.3: A Sample of the Details Table

Customer

Number

Inter-Arrival

Time

Clock Time Of

Arrival

Clock Time

Service Starts

Server Number To

Perform The

Service

Duration Of

Service

1 1.1881 1.1881 1.1881 Server 1 0.49442 0.3703 1.5584 1.5584 Server 2 0.7515

3 0.2300 1.7884 1.7884 Server 1 0.0587

Table 4.3 represents a sample of the Details Table in the simulation program. Table is used to

show which columns will be used in the following comparison.

Added to the comparison in Section 4.3, the averages of the:

Inter-arrival time

Duration of service,

were found by using the Detailed Results table in the “Detailed results” spreadsheet. By

comparing the Averages in the detailed results table against the actual values used to perform the

simulation, a variation can be found. Even though the random times generated are different to

the original inputs, due to the distributions, the averages are similar to the original values that

were inputted. The comparisons are shown in Table 4.4 for all of the distributions available

within the model. The comparison above focus’s on the inputs of the environment.



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Table 4.4: Input time versus simulated time

Description Run 1 Run 2 Run 3 Run 4 Run 5

Distribution Exponential Constant Normal Triangular Observed

Traffic Intensity 0.75 0.75 0.83 0.99 0.85

Inter-Arrival timeinserted by user

Average0.0400

Average2.0

Average0.40

Std Deviation0.1

Minimum 1Most Likely 2

Maximum 3

Prob Time0.7 50.1 40.1 30.1 2

Average4.40

Average simulatedinter-arrival time

0.0406 2.0 0.37 1.91 4.23

Variat ion 0.0006 0.000 0.03 0.09 0.17

Service time insertedby the user

Average0.0300

Average1.5

Average2.00

Std Deviation0.5

Minimum 5Most Likely 6

Maximum 7

Prob Time0.1 40.2 60.2 70.5 9

Average 7.5

Average simulatedservice time

0.0290 1.5 2.05 5.96 7.45

Variat ion 0.0010 0.000 0.05 0.04 0.05

The simulated results as shown in Table 4.4 appear to be similar to the analytical results. That

gives confidence that the simulator simulates the times correctly. A further check would be totest the simulated times for statistical significant deviation from the expected values. This has

been done for the observed distribution in Table 4.5.

Table 4.5: Statistical comparison

Description Inter-Arrival Time Service Time

Average Time 4.400 7.500Samp le Size 47 47

Standard Deviat ion 1.020 1.688

Signif icanc e Level 0.05 (95%) 0.05 (95%)

Confid ence Interval

High 4.692 7.983

Low 4.108 7.017

The observed inter-arrival time of 4.23 falls well in to the 95% confidence interval, and so does

the simulated service time of 7.45. This indicates that the observed probability distribution



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seems to be simulated correctly. An alternative statistical test would have been to do a

goodness-of-fit test on the observed simulated times.

4.5 SUMMARY

It can be seen that there is a small variation between the simulated results and the analytical data.

Both the input data e.g. inter-arrival time, and the output results e.g. number of clients in queue,

are similar when comparing the theoretical data and the simulated results. A conclusion can be

drawn: the simulated results proves to be within a reasonable accuracy when compared to the

analytical results.



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CHAPTER 5

5. USER GUIDE

5.1 INTRODUCTION

The following section will explain systematically what each button will do when activated.

When loading the Excel simulation file, the user will be prompted to enable the built in macro’s:

The macro’s must be enabled, for the program to work. Once the macro’s have been enabled,

the user will be presented with a Welcome screen (Figure 5.1).

5.2 USING THIS GUIDE

New and experienced users of Microsoft Excel may use this manual. The user will be able to

simulate basic queuing scenario’s. The program is written in a friendly format using a quasi form

of wizard that will try to attempt to catch any incorrect information where possible. The manual

will help the user will be able to use this program by making use of this manual.

Some of the screens are password protected. To unprotect a screen, use the “usb” password. The

password is caps sensitive.

It is compulsory to place information in the input boxes. If the boxes are not completed as

required, with the result of information being omitted, the simulation program will inform the

user to re-enter the required data. The appropriate input box will automatically be displayed.



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5.3 CONTROL CENTRE

Figure 5.1: Welcome Screen

Press the button to activate the central control menu.

After clicking the Central Control Menu button the following Figure 5.2 appears:



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Figure 5.2: Control Centre

The control centre screen is divided up into two main sections:

Action buttons: These buttons are used to start a process

Navigation buttons: These buttons are used to navigate from screen to screen.

On the Control Panel a indicator box called “Number of History Space Left” shows the number

of spaces the user has left to record simulated results. For example, if the box displays the

number 3, it means that the user may save three more models out of a total of five saves.



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5.4 ACTIONS BUTTONS

5.4.1 “Change Inputs” Button

The “Change Inputs” Button is used when the user wants to edit the current data used by

the program to run the simulation. After the change inputs button is pressed, Figure 5.3

appears on the screen.

The information button presents information as to what is required by the input boxes.

Figure 5.3: Input Screen

The input screen requires the following information:

a) The unit of T ime

The unit of time option allows the user to select the time unit he/she would prefer to use when

running the simulation.

The options are:

Minute

Hour



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Day

b) The number of uni ts that the simulation must run

The number of units that the simulation must run limits the number of observations to generate.

For example, if the units are hours, the arrival rate is 20 per hour, the limit is set to 8 hours as in

a working day then the result will be approximately 160 observations. The higher the limit, the

closer the result will be to the analytical result, however the system takes much longer to

simulate as the time is increased.

c) The number of servers

In the input box, the number of servers must be specified. If, for example two bank tellers are

used to service clients then the number 2 must be inserted in the box.

d) The maximum number of customers all owed in the queue.

The program allows the option of either having an unlimited number of space available for the

customers to queue (setting equals a 1000) or a limited amount of space. It would be used when

the area in which to queue can only hold, for example, 20 customers, the setting would be set to

20. The system now rejects any customer that enters the system if the queue length in longer

than 20.

Once the relevant data has been entered and the continue key clicked, the following screen

appears (Figure 5.4).



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Figure 5.4: Inter-arrival Input Box

The screen above is the Inter-arrival Input Screen. In the Figure 5.4, the following must be

updated.

e) I nput the inter-arr ival time

If customers arrive at a rate of 12 per hour, then find the reciprocal of 12 to get the inter-arrival

time i.e. 1/12 =0.0833 hours or 5 minutes, is the number entered in the box. The time is used to

simulate the environment specified by the user.

f) Select a distri bution pattern.

Different distribution patterns are selected for the inter-arrival times. The following options are

available:

Exponential

Constant

Normal

Triangular

Observed Probability

The Observed Probability option is important as the program will check this parameter and do

the calculations based on the distribution pattern specified.

Once the relevant data has been entered, click the continue key and the following service inputs

screen will appear (Figure 5.5):



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Figure 5.5: Service Inputs

In the Service Inputs screen the user will select the following

g) I npu t the average service time per server

If customers are serviced at a rate of 6 per hour, then find the reciprocal of 6 to get the service

time per server i.e. 1/6 = 0.166 hours or 10 minutes, is the number entered in the box. Time is

used to simulate the environment specified by the user.

h) Select a distr ibution pattern.

Different distribution patterns for the average service time per server are the same as the options

for the inter-arrival rate (see point f). Once the appropriate distribution pattern has been

selected, press the "Continue"-button. The input screens for changing or adding data are now

complete. The user will be returned to the last screen he/she was viewing.

5.4.2 “Run Simulation” Button

The "Run Simulation"-button initiates the simulation process. The program will effectively

calculate all relevant information and post it to the different sheets. (See Program Logic).



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5.4.3 “Update Probability Tables” Button

The “Update Probability Tables”-button takes the user to the probability table screen. Here the

user will enter the observed probabilities for both the arrival time and the service time.

Figure 5.6: Probability Table

Probability: Add the relevant probability in relation to the average Inter-arrival or Service time.

Specific Inter-arrival / Service time: Add the inter-arrival or service time to the corresponding

probability.

Note: the cumulative probability must add to the value one. If not, the program will not run.

The program checks the cumulative probability of both the Arrival and Service times. If either of

the two probabilities of times do not add to one, the program stops and returns to the Probability

Table screen (Figure 5.4), so that the user may make the appropriate amendments. If a value is

entered in the average inter-arrival time box (Paragraph 5.4.1, point e), the program will ignore

the value and replace it with the average of the inter-arrival times, which is shown in the arrival

probability table in Figure 5.6. The average will be shown in Input Screen, however it will not be

used in the simulation program. Only inter-arrival times calculated by generating random

numbers, and finding the corresponding time, in the probability table, will be used.



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5.4.4 “Add to History File” Button

The "Add to History File"-button allows the program to add / save simulated results in a

spreadsheet. It allows the user to save up to five simulated runs. First, clear the history file by

pressing the “Clear History” button (Paragraph 5.4.4). Then run a simulation. Once the

simulation has run, press the “Add To History File” button and it will save it to the history

screen. Refer to Fig 5.7.

Figure 5.7: History Screen

5.4.5 “Clear History” Button

The “Clear History” button is used to clear all the data on the history screen.

5.4.6 “Restore and Hide” Buttons

The “Restore and Hide” buttons are used to hide or show all the toolbars, status’s bars etc. The

restore/hide feature allows the user to have access to the model, so that changes can be made to

the model.



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5.5 NAVIGATION BUTTONS

The navigation buttons are used to navigate from screen to screen. Each screen represents a set

of data and it is as follows:

(Please check the Appendix B for a list of all the screens for a more detailed description.)

a) Welcome Screen

The Welcome screen is the introduction screen.

b) The I nput Screen

The Input screen shows all the relevant inputs used for the simulation program except for the

observed probabilities.

c) The Report Screen

The Report screen shows the following information:

User statistics

System orientated statistics

Probability distribution of number in queue.

d) The H istory Screen

The History screen shows a list of up to five saved simulated runs.

e) The Chart Screen

The Chart screen shows the results in form of charts

f) The Probabil i ty Chart Screen

The Probability Chart screen shows one chart that represents the probability distribution of the

number of customers in the queue.



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g) The Detailed Resul ts Screen

The Detailed Results screen shows information about each customer and each server.

h) The Summar y Screen.

The Summary screen shows a summary of the server idle time and the average customer waiting

time.

5.6 SUMMARY

The user guide covers the navigation of simulation program. An important characteristic, of the

simulation program to remember is, only times, should be inputted when prompted for arrival or

service durations. The other information is self-explanatory. The sequence of usage is irrelevant

i.e. any button may be clicked to see what it does. When trying to run a simulation for the users

environment, the “Change Inputs” button must be clicked followed by the “Run simulation”

button.



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CHAPTER 6

6. SUMMARY AND RECOMENDATIONS

6.1 SUMMARY

The core of this study project consists of a queuing simulation model that was built in the Excel

environment with visual basic. The model allows a user to run many variations of an

environment that he/she would like to improve. Topics, covered by the document, are from the

input stage to the output stage and how to use the results. Computer simulation is one of the

most versatile of all management science tools, and its popularity is growing constantly. The

simulation model demonstrated how the random function in Excel allows a user to simulate a

wide variety of problems. However, it only represents a small fraction of what simulation can

accomplish. However, the users should come away with an increased understanding of the

concept of simulation.

6.2 RECOMMENDATIONS

To enhance the simulation experience the user could take advantage of a powerful add-in

package, @RISK, that facilitates simulation (not for queuing), particularly statistics gathering

and presentation of results. The add-in, along with the functionality of Excel itself, allows

individuals with virtually no programming skills to perform complex and realistic simulations.

Even this, however, is only the tip of the iceberg in terms of what simulation can accomplish.

There are many special-purpose simulation packages that can simulate complex queuing systems

and a variety of other processes, and these packages are being, using increasingly often in the

business world. The material covered in this document should give the user a start in the use

simulation, however the extent to which simulation is used in the working environment is

extremely large and complex!



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LIST OF SOURCES

Winston, W.L. & Albright, S.C. 1997. Practical Management Science: Spreadsheet Modelling

and Applications. Belmont, CA: Duxbury

Turban, E. & Meredith, J.R. 1994. Fundamentals of Management Science. 6th ed. BurrRidge,

Ill: Irwin

Microsoft Corporation. 1999. Excel spreadsheet. Version 2000.



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APPENDIX A: LIST OF ROUTINES AND THEIR FUNCTIONS



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LIST OF ROUTINES AND THEIR FUNCTIONS

Visual Basic Routine It's function

ServDist_Change The routine prompts the user for either the standard deviation or the min, mostlikely and maximum value depending on what the user chose as the distributionprocess

GetInputs The routing calls up the input boxes for the program

RunSimulation It is the main routine that will run the simulation and call other routines toaccomplish the end result

Finishoff The routine does some formatting for presentation

Averages It creates the averages for the work stations in form of a pivot table in thesummary sheet

Check Checks for blanks and fills it with Zeros

Initialize Resets the sub routine parameters to zero start a new simulation

Timing Finds the most imminent event and record the server that has just finished

Arrive Calculates the Arrival time

Depart Calculates the Departure Time

Report Creates the Report Sheet

UpdateAreas Updates the report sheet

Buildreportsheet Creates the final details report sheet

Queuelength Determines the queue length and inserts it in the appropriate spread sheet

Auto_Close Runs when Excel closes. It restores the Excel sheets

Auto_Open Runs when Excel Opens. It removes toolbars starts sets the environment

GoToReport Takes the user to the Report sheet

CreateChart Creates the probability chart

GoToInputs Takes the user to the Inputs sheet

GeneralInputs Inserts the users inputs into the sheets

ArrivalInputs Inserts the arrival inputs

ServiceInputs Inserts the Service inputs

MaxInQueue_AfterUpdate Calls an information box

GoToCharts Takes user to the chart sheet

GoToHistory Takes user to the History sheet

ClearHistory It clears the history sheet to enable new data to be inputted

AddToHistory It adds data that has been recently run to the history sheet

SetNoOfRuns Sets the number of runs in the history sheet

PrintInputs Prints the Inputs spread sheet

PrintReports Prints the Reports spread sheet

PrintProbtables Prints the Probability table spread sheet

PrintHistory Prints the History spread sheet

PrintGraphs Prints the Graphs spread sheet

ArrDist_Change Shows or hides information which is appropriate or not appropriate at the timeof running the simulation



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APPENDIX B: LIST OF SCREENS



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LIST OF SCREENS

B.1 WELCOME SCREEN

Figure B.1: Welcome Screen

a) The Purpose of thi s screen

The Welcome Screen is the default introductory screen, which serves as an introduction screen.

By clicking on the Central Control Menu Button, the user may navigate to any other screen

within the application.

b) How to interpret the information on the screen

The Welcome Screen has no use, other than informing the user of:

The title of the package

The program used

The writer of the program.



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B.2 INPUTS SCREEN

Figure B.2: Inputs Screen


The Inputs Screen shows the inputs that will be used by the program for simulation purposes.


The user can use the screen for:

To check that the information used is as per the environment simulated.



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B.3 REPORTS SCREEN

Figure B.3: Reports Screen


The Reports Screen shows some of the outputs generated by the program.


Under the sub headings of the screen the following information can be used:

User Statistics

The user statistics information pertains to the individual i.e. the customer (See 2.2.1). It will help

in determining how the queuing environment affects the customer. All these results must be

minimised if possible.

Queue orientated statistics

The queue orientated statistics information pertains to the queue that is formed within the

environment. That the information supplied is concerning the queue and not the entire system.



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The information supplied by the program must be compared to the desired results of the

management of the queuing environment so that a compromise can be sought.

Probability of distribution number in queue

The “probability of distribution number in queue” information pertains to the queue that is

formed within the environment. The information supplied is concerning the queue and not the

entire system



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B.4 MULTI-GRAPH SCREEN

Figure B.4: Graphical representation of Results


The Graphical representation of Results screen shows some of the outputs generated by the

program in graphical format.


The Graphical representation of Results screen is useful for those users who like a quick

overview (“feel”) of the results. In the example above (Figure B.4, top, right graph), the vast

difference between the maximum customers in the queue and the average number in the queue

can be seen. It will help in formulating the size of the area, which should be provided for the

queue.



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B.5 GRAPHICAL DISTRIBUTION SCREEN

Figure B.5: Graph of Distribution Pattern


The Graph of Distribution Pattern screen shows some of the outputs generated by the program in

graphical format.


The Graph of Distribution Pattern screen is useful for those users who like a quick overview

(“feel”) of the results. In this example, just over 60% of the people will not have to queue in this

particular environment.



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B6. DETAILS SCREEN

Figure B.6: Detail Screen


The Detail Screen shows some of the detailed outputs generated by the program. Note that the

user will have to scroll to the right to get to the Central Control Panel.


The Detail Screen presents the following information about the Queue:

Customer Number

It shows the customer number in the sequence of arrival.

Inter-arrival time

It shows the randomly generated inter-arrival time generated by the program

Clock time of arrival



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In form of a continuous clock, the time of arrival is calculated, by adding the randomly generated

inter-arrival time to the last arrival time.

Time service starts

In form of a continuous clock, the time of the service start is shown. The time is based on First

come First served i.e. the first available server will take on a new customer. The model checks

for servers that are idle, and of those servers that are idle, it will assign the client to the server

with the lowest number i.e. server two will get preference over server three and four etc.

Server number to perform the service

Shows the server number that serviced the customer.

Duration of service

Show the duration of the service. The service time is randomly generated.

Clock time the service ends

The “clock time the service ends” time is based on the randomly generated duration of service

time i.e. “Time service start” plus “Duration of service” equals “Clock time the service ends”.

Waiting time of customer in minutes

If the customer waits then the time waited is recorded in this field

Queue length

The field shows the queue length at the point where the customer enters the system.

The rest of the information is the same as what is in the blue table expert for the last column in

the green table. The column shows the idle time for each server.



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B.7 AVERAGES SCREEN

Figure B.7: Averages Screen


The Averages screen shows the averages of the simulated data, which was generated by the

program.


The user can quickly see when more servers are added, the idle time increase as the number of

servers is increased.



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APPENDIX C: VISUAL BASIC CODE



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VISUAL BASIC CODE

Option Explicit

Option Base 1

'Define all the variables that will be used across routines

Dim i As Integer

Dim Nextcell, numberoftoolbars As Single, Nextcust As Integer, serverno As Integer, timingcount As Single

Dim AvgDelay, AvgNumInQ, StdDevArrive, StdDevService, Randomnum, MostLikelyValue, _

MinimumValue, ServiceSeq, MaximumValue, StdCArrive, StdCService, ValA, ValB, ServDist, ArivDist As

Double

Dim MaxInQ As Integer

Dim NextEventType As Integer, NumInQ As Integer, _

NumCusts As Long, NumBusy As Integer, _

numservers As Integer, FinishedServer As Integer, _

MaxInSys As Integer, NumLost As Integer

Dim AreaNumInQ As Single, AreaUtil As Single, MaxDelay As Single, _

TimeArrival(1000) As Single, Time As Single, TimeLastEvent As Single, _

TotDelays As Single, TimeNextEvent() As Single

Dim TimeInQ(0 To 1000) As SingleDim MeanArriveTime As Single, MeanServeTime As Single, _

MaxTime As Single

' Calculate the steady-state probability that no customers are in the

' system - this is needed for the steady-state outputs shown on the

' Report sheet

Function ProbEmpty(arrivetime As Single, servetime As Single, _

numservers As Integer) As Single

Dim Sum As Double, Product As Double, i As Integer, _

Traffic As Single

Traffic = servetime / (numservers * arrivetime)

If numservers = 1 Then

ProbEmpty = 1 - TrafficElse

Product = 1

Sum = 1

For i = 1 To numservers - 1

Product = Product * numservers * Traffic / i

Sum = Sum + Product

Next

Product = Product * Traffic / (1 - Traffic)

Sum = Sum + Product

ProbEmpty = 1 / Sum

End If

Worksheets("reports").Range("probempty").Value = ProbEmpty

End Function

Sub GetInputs()

Dim ArriveRate As Single, arivedist, servdist, arrivedist1 As Single, ServeRate As Single

Dim MaxTime As Single, numservers As Integer

Dim MaxInSys As Integer, timeunit As String

Dim checkforo As Single

Worksheets("Inputs").Range("ArriveTime").Value = 0

Worksheets("Inputs").Range("serveTime").Value = 0

'call msg boxes

DialogSheets("QGeneral Inputs").EditBoxes("NoOfUnits").Text = 0DialogSheets("QGeneral Inputs").EditBoxes("NumService").Text = 0

DialogSheets("QGeneral Inputs").EditBoxes("MaxInQueue").Text = 0



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DialogSheets("QGeneral Inputs").Show

DialogSheets("QArrival Inputs").EditBoxes("AvgCustArrive").Text = 0

Worksheets("Inputs").Range("ArivDist").Value = 1

DialogSheets("QArrival Inputs").Show

DialogSheets("QService Inputs").EditBoxes("AvgCustService").Text = 0

Worksheets("Inputs").Range("ServDist").Value = 1

DialogSheets("QService Inputs").Show'check if probs = 1

checkforo = Worksheets("Inputs").Cells(4, 6).Value

Do Until checkforo > 1

arivedist = Worksheets("Inputs").Range("ArivDist").Value

If arivedist = 5 Or 4 Then

Worksheets("Inputs").Range("ArriveTime").Value =

Worksheets("Inputs").Range("MostLikArrive").Value

Else

MsgBox "Note: You have selected a Zero Value for the Arrival time. The program cannot run with a zero

value. Please insert a value greater than one!"

DialogSheets("QArrival Inputs").EditBoxes("AvgCustArrive").Text = 0DialogSheets("QArrival Inputs").Show

End If


Loop


Do Until checkforo > 1

servdist = Worksheets("Inputs").Range("ServDist").Value

If servdist = 5 Or 4 Then

Worksheets("Inputs").Range("serveTime").Value = 1

ElseMsgBox "Note: You have selected a Zero Value for the Service time. The program cannot run with a zero

value. Please insert a value greater than one!"

DialogSheets("QService Inputs").EditBoxes("AvgCustService").Text = 0

DialogSheets("QService Inputs").Show

End If


Loop

'warn user of prob 1

arrivedist1 = Worksheets("Inputs").Range("ArivDist").Value

Select Case arrivedist1Case 1, 2, 3, 4

Case 5

MsgBox ("You have selected the 'Observed Probabilities' distribution option for the inter-arrival time,

please Update the Arrival Probability Table before you run the simulation.")

Worksheets("Observed Prob").Select

Worksheets("Observed Prob").Cells(1, 1).Select

Case Else

End Select

arrivedist1 = Worksheets("Inputs").Range("servDist").Value

Select Case arrivedist1

Case 1, 2, 3, 4



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Case 5

MsgBox ("You have selected the 'Observed Probabilities' distribution option for the service time per server,

please Update the Service Probability Table before you run the simulation.")



Case Else

End Select

DialogSheets("Navigation Bar").hide

End Sub

Sub RunSimulation()

Dim arivedist, servdist As Integer

' check if prob = 1 if not abort

arivedist = Worksheets("Inputs").Range("ArivDist").Value


If arivedist = 5 Or servdist = 5 Then


Dim checking As Single

checking = Worksheets("Observed Prob").Cells(14, 2).Value

If checking < 1 Then

If checking = 0 Then

Else

MsgBox "You have selected the 'Observed Probabilities' as your distribution, however the arrival

probability total must add up to one. Please correct any errors."

Worksheets("Observed Prob").Cells(3, 2).SelectDialogSheets("Navigation Bar").hide ' hide bar

Exit Sub

End If

Else


Else

MsgBox "You have selected the 'Observed Probabilities' as your distribution, however the arrival



DialogSheets("Navigation Bar").hide ' hide bar

Exit Sub

End If

End If

checking = Worksheets("Observed Prob").Cells(14, 6).Value

If checking < 1 Then


Else

MsgBox "You have selected the 'Observed Probabilities' as your distribution, however the service




Exit Sub

End If

Else


Else



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MsgBox "You have selected the 'Observed Probabilities' as your distribution, however the service




Exit Sub

End If

End If

Else

End If

If arivedist = 5 Then

Worksheets("Inputs").Range("ArriveTime").Value = Worksheets("Observed

Prob").Range("Averagearrival").Value

MsgBox "Note: You have chosen the Average Arrival Time as the distribution pattern. The Average of

the times will be displayed (for reporting purposes) on the input screen as 'Average time between arrivals',

however this average will not be used in the simulation."

End If

If servdist = 5 ThenWorksheets("Inputs").Range("ServeTime").Value = Worksheets("Observed

Prob").Range("Averageserve").Value

MsgBox "Note: You have chosen the Average Service Time as the distribution pattern. The Average of

the times will be displayed (for reporting purposes) on the input screen as 'Average time for each service',

however this average will not be used in the simulation."

End If

'get user inputs from Inputs screen

Application.ScreenUpdating = True

With Worksheets("Inputs")

MeanArriveTime = .Range("ArriveTime").ValueMeanServeTime = .Range("ServeTime").Value

numservers = .Range("NumServers").Value

MaxInSys = .Range("MaxInSys").Value

MaxTime = .Range("MaxTime").Value

End With

ReDim TimeNextEvent(numservers + 1)

Nextcell = 1

Initialize

Do

Nextcell = Nextcell + 1

Timing ' Find the time, type of next event, reset clock

UpdateAreas ' Update statistical accumulators

If NextEventType = 1 ThenArrive ' subroutine for an arrival

Else

Depart ' subroutine for a departure (service completion)

End If

' Cut off all future arrivals if store's doors have closed

If Time > MaxTime And TimeNextEvent(1) < 100000 Then

TimeNextEvent(1) = 100000

End If

Loop Until Time > MaxTime And NumBusy = 0

check ' fill blanks with zero's

finishoff ' format table

Averages ' find averages

queuelength ' find queue length

buildreportsheet ' biuld detail table



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Report ' Put the outputs on the Report sheet

CreateChart ' create chart

Worksheets("Reports").Select ' goto reports sheet


End Sub

Sub finishoff()

Dim count As Single

count = NumCusts + 2

Worksheets("table2").Select

' format table

Range(Cells(3, 1), Cells(count, 6)).Select

Selection.Copy

Range("G3").Select

Selection.PasteSpecial Paste:=xlValues, Operation:=xlNone, SkipBlanks:= _

False, Transpose:=False

Range(Cells(2, 7), Cells(count, 11)).Select

Application.CutCopyMode = FalseSelection.Sort Key1:=Range("K3"), Order1:=xlAscending, Key2:=Range("I3") _

, Order2:=xlAscending, Header:=xlGuess, OrderCustom:=1, MatchCase:= _

False, Orientation:=xlTopToBottom

Range("L3").Select

ActiveCell.FormulaR1C1 = "0"

Range("L4").Select

ActiveCell.FormulaR1C1 = "=RC[-3]-R[-1]C[-2]"

Range("L4").Select

Selection.AutoFill Destination:=Range(Cells(4, 12), Cells(count, 12)), Type:=xlFillDefault

Worksheets("Table2").Cells(3, 12).Value = Worksheets("Table2").Cells(3, 9).Value

count = 0

Dim nextcustomer As Single

Do Until count = NumCusts

'find blanks and fill

nextcustomer = Worksheets("Table2").Cells(3 + count, 12).Value

If nextcustomer < 0 Then

Worksheets("Table2").Cells(3 + count, 12).Value = 0

Else

End If

count = count + 1

Loop

End Sub

Sub Averages()

'find averages

Worksheets("Summary").Select

ActiveSheet.PivotTables("PivotTable").PivotSelect "", xlDataAndLabel

Selection.ClearContents

Rows("7:16").Select

Selection.Delete Shift:=xlUp


'calculate customer delay

Range(Cells(3 + NumCusts, 6), Cells(3 + NumCusts, 6)).Select

ActiveCell.FormulaR1C1 = "=AVERAGE(R[-" & NumCusts & "]C:R[-1]C)"

Worksheets("Summary").Cells(2, 2).Value = Worksheets("Table2").Cells(3 + NumCusts, 6).Value

Range(Cells(3 + NumCusts, 6), Cells(3 + NumCusts, 6)).ClearContents



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'calculate server delay


Dim myRange As Single

myRange = 2 + NumCusts

ActiveSheet.PivotTableWizard SourceType:=xlDatabase, SourceData:= _

"Table2!R2C11:R" & myRange & "C12", TableDestination:= _"'[Queuing simulation New.xls]Summary'!R7C1", TableName:="PivotTable"

ActiveSheet.PivotTables("PivotTable").AddFields RowFields:="Server Number"

ActiveSheet.PivotTables("PivotTable").PivotFields("Idle Time of Each Server").Orientation _

= xlDataField

ActiveSheet.PivotTables("PivotTable").ColumnGrand = False

ActiveSheet.PivotTables("PivotTable").PivotFields("sum of Idle Time of Each Server"). _

Function = xlAverage

Cells.Select

Selection.Interior.ColorIndex = 43

Columns("A:A").Select

Selection.Font.Bold = False

Selection.Font.Bold = True

Columns("B:B").SelectSelection.Font.ColorIndex = 6

Selection.Font.Bold = False

Selection.Font.Bold = True

Range("A1").Select

Columns("A:A").EntireColumn.AutoFit

Columns("A:A").Select

Selection.Font.ColorIndex = 2


Range("A1").Select

End Sub

Sub check()

'check for zeros

Dim count As Single, nextcustomer As Single, nextcustomer1 As Double

count = 0

Do Until count = NumCusts

nextcustomer = Worksheets("Table2").Cells(3 + count, 2).Value

nextcustomer1 = Worksheets("Table2").Cells(3 + count, 6).Value

If nextcustomer


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Dim i As Integer

Time = 0

NumBusy = 0

NumInQ = 0

TimeLastEvent = 0

serverno = 0

NumCusts = 0 NumLost = 0

TotDelays = 0

MaxDelay = 0

AreaNumInQ = 0

MaxInQ = 0

AreaUtil = 0

Nextcust = 1

timingcount = 0

Worksheets("Table2").Range("Clearcontents").ClearContents

'rest parameters

Worksheets("Reports").Range("NumLost") = 0

Worksheets("Reports").Range("NumCusts") = 0

Worksheets("Reports").Range("MaxDelay") = 0Worksheets("Reports").Range("AvgDelay") = 0

Worksheets("Reports").Range("AvgNumInQ") = 0

Worksheets("Reports").Range("MaxInQ") = 0

Worksheets("Reports").Range("Util") = 0

arivdist = Worksheets("Inputs").Range("ArivDist").Value

Select Case arivdist ' Evaluate ArivDist

Case 1 ' Case for Poisson and Exponetial

' Schedule an arrival from the exponential distribution

TimeNextEvent(1) = -MeanArriveTime * Log(Rnd)

Case 2 'Case for Constant distribution

TimeNextEvent(1) = MeanArriveTime

Case 3 ' Case for Normal Distribution

StdDevArrive = Worksheets("Inputs").Range("StdDevArrive").Value

MeanArriveTime = Worksheets("Inputs").Range("ArriveTime").Value

Randomnum = Rnd

meanarrivetime2 = MeanArriveTime

MeanArriveTime = Application.WorksheetFunction.NormInv(Randomnum, StdDevArrive,

MeanArriveTime)Do Until MeanArriveTime > 0

Randomnum = Rnd


meanarrivetime2)

Loop

MeanArriveTime = MeanArriveTime

TimeNextEvent(1) = MeanArriveTime

Case 4 ' Case Triangular

Randomnum = Rnd

MostLikelyValue = Worksheets("Inputs").Range("MostLikArrive").Value

MinimumValue = Worksheets("Inputs").Range("MinArriveValue").Value

MaximumValue = Worksheets("Inputs").Range("MaxValueArrive").Value

StdCArrive = Worksheets("Inputs").Range("StdCArrive").Value



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If Randomnum


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' Schedule an arrival from the exponential distribution

TimeNextEvent(1) = Time - MeanArriveTime * Log(Rnd)


TimeNextEvent(1) = Time + MeanArriveTime


StdDevArrive = Worksheets("Inputs").Range("StdDevArrive").Value

MeanArriveTime = Worksheets("Inputs").Range("ArriveTime").Value

Randomnum = Rnd

meanarrivetime2 = MeanArriveTime


MeanArriveTime)

Do Until MeanArriveTime > 0

Randomnum = Rnd


meanarrivetime2)

LoopMeanArriveTime = MeanArriveTime

TimeNextEvent(1) = Time + MeanArriveTime


Randomnum = Rnd

MostLikelyValue = Worksheets("Inputs").Range("MostLikArrive").Value

MinimumValue = Worksheets("Inputs").Range("MinArriveValue").Value

MaximumValue = Worksheets("Inputs").Range("MaxValueArrive").Value

StdCArrive = Worksheets("Inputs").Range("StdCArrive").Value


If Randomnum MaxInQ Then

MaxInQ = NumInQ

End If

' Keep track of each customer's arrival time (for later stats)

TimeArrival(NumInQ) = Time



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' Otherwise, customer can go directly into service

Else

' Make the first idle server busy and schedule a departure

NumBusy = NumBusy + 1

i = 2

SchedDep = TimeNextEvent(i)

' This loop searches for the first idle serverDo

If SchedDep > 99999 Then

ServiceSeq = 1

'Determine the Service Distribution

'schedule an Service based on users input


' Stop

Select Case servdist ' Evaluate ServDist


' Schedule an Service from the exponential distribution

If ServiceSeq = 1 ThenTimeNextEvent(i) = Time - MeanServeTime * Log(Rnd)

Else

Stop

TimeNextEvent(FinishedServer) = Time - MeanServeTime * Log(Rnd)

End If


If ServiceSeq = 1 Then

TimeNextEvent(i) = Time + MeanServeTime

Else

TimeNextEvent(FinishedServer) = Time + MeanServeTime

End If


StdDevService = Worksheets("Inputs").Range("StdDevService").Value

MeanServeTime = Worksheets("Inputs").Range("ServeTime").Value

Randomnum = Rnd

meanservetime2 = MeanServeTime

MeanServeTime = Application.WorksheetFunction.NormInv(Randomnum, StdDevArrive,

MeanServeTime)

Do Until MeanServeTime > 0

Randomnum = Rnd

MeanServeTime = Application.WorksheetFunction.NormInv(Randomnum, StdDevArrive,

meanservetime2)

LoopMeanServeTime = MeanServeTime



Else


End If


Randomnum = Rnd

MostLikelyValue = Worksheets("Inputs").Range("MostLikService").Value

MinimumValue = Worksheets("Inputs").Range("MinServiceValue").Value

MaximumValue = Worksheets("Inputs").Range("MaxValueService").Value

StdCService = Worksheets("Inputs").Range("StdCService").Value

ValB = (MaximumValue - MinimumValue)



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If Randomnum 0 And i > 0 Then

'update table

Worksheets("Table2").Cells(2 + Nextcust, 1).Value = Nextcust

Worksheets("Table2").Cells(2 + Nextcust, 4).Value = TimeNextEvent(i)

Worksheets("Table2").Cells(2 + Nextcust, 3).Value = starttime

Worksheets("Table2").Cells(2 + Nextcust, 5).Value = "server " & serverno

Nextcust = Nextcust + 1

Else

End If

End Sub

Sub Depart()

Dim i As Integer, Delay As Single, starttime As Double, servetemp As Double, numberone As Double,

numbertwo As Double

servetemp = serverno

' Update number of customers who have finished

NumCusts = NumCusts + 1



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' Check if any customers are waiting in queue - if not, make the

' server who just finished idle by resetting the TimeNextEvent to a

' large number

If NumInQ = 0 Then

NumBusy = NumBusy - 1TimeNextEvent(FinishedServer) = 100000

' Otherwise, take customer from front of queue into service

Else

NumInQ = NumInQ - 1

'Worksheets("Table2").Cells(2 + Nextcust, 13).Value = NumInQ

' Delay is the time this customer has been waiting in line

Delay = Time - TimeArrival(1)

If Delay > MaxDelay Then

MaxDelay = Delay

End IfTotDelays = TotDelays + Delay

AvgDelay = TotDelays / NumCusts

'Worksheets("Reports").Range("AvgDelay").Value = AvgDelay

'Worksheets("Reports").Range("MaxDelay").Value = MaxDelay

' Schedule departure for this customer with the same server who just

' finished

ServiceSeq = 2

i = 2

'Determine the Service Distribution

'schedule an Service based on users inputservdist = Worksheets("Inputs").Range("ServDist").Value

Select Case servdist ' Evaluate ServDist


' Schedule an Service from the exponential distribution


TimeNextEvent(i) = Time - MeanServeTime * Log(Rnd)

Else

TimeNextEvent(FinishedServer) = Time - MeanServeTime * Log(Rnd)

End If

Case 2 'Case for Constant distributionIf ServiceSeq = 1 Then


Else


End If


StdDevService = Worksheets("Inputs").Range("StdDevService").Value

MeanServeTime = Worksheets("Inputs").Range("ServeTime").Value

Randomnum = Rnd

meanarrivetime2 = MeanServeTime

MeanServeTime = Application.WorksheetFunction.NormInv(Randomnum, StdDevService,

MeanServeTime)



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Do Until MeanServeTime > 0

Randomnum = Rnd

MeanServeTime = Application.WorksheetFunction.NormInv(Randomnum, StdDevService,

meanarrivetime2)

Loop

MeanServeTime = MeanServeTime

If ServiceSeq = 1 ThenTimeNextEvent(i) = Time + MeanServeTime

Else


End If


Randomnum = Rnd

MostLikelyValue = Worksheets("Inputs").Range("MostLikService").Value

MinimumValue = Worksheets("Inputs").Range("MinServiceValue").Value

MaximumValue = Worksheets("Inputs").Range("MaxValueService").Value

StdCService = Worksheets("Inputs").Range("StdCService").Value

ValB = (MaximumValue - MinimumValue)

If Randomnum 0 And i > 0 Then

serverno = FinishedServer - 1

'update tables

Worksheets("Table2").Cells(2 + Nextcust, 6).Value = Delay

Worksheets("Table2").Cells(2 + Nextcust, 1).Value = Nextcust

Worksheets("Table2").Cells(2 + Nextcust, 4).Value = TimeNextEvent(FinishedServer)

Worksheets("Table2").Cells(2 + Nextcust, 3).Value = starttime

Worksheets("Table2").Cells(2 + Nextcust, 5).Value = "server " & serverno

Worksheets("Table2").Cells(2 + Nextcust, 2).Value = starttime - Delay



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Nextcust = Nextcust + 1

serverno = FinishedServer + 1

Else

End If

' Move everyone else in line up one space

For i = 1 To NumInQTimeArrival(i) = TimeArrival(i + 1)

Next

End If

End Sub

Sub Report()

'ActiveWorkbook.Protect Password:="usb", structure:=False, Windows:=False

Dim i As Integer

Dim AvgDelay As Single, AvgNumInQ As Single, Util As Single

AvgDelay = TotDelays / NumCusts

AvgNumInQ = AreaNumInQ / Time

Util = AreaUtil / Time

Time = 0

For i = 0 To MaxInQ

Time = TimeInQ(i) + Time

Next

For i = 0 To MaxInQ

TimeInQ(i) = TimeInQ(i) / Time

Next

With Worksheets("Reports")

.Activate

.Range("NumCusts").Value = NumCusts.Range("AvgDelay").Value = AvgDelay

.Range("MaxDelay").Value = MaxDelay

.Range("AvgNumInQ").Value = AvgNumInQ

.Range("MaxInQ").Value = MaxInQ

.Range("Util").Value = Util / numservers

.Range("NumLost").Value = NumLost

' TimeInQ records, for value of NumInQ (0 to MaxInQ) the percentage

' of time that many customers were waiting in the queue

.Range("NumInQ").ClearContents

.Range("TimeInQ").ClearContents

.Range("diference").ClearContents

End With

With ActiveWorkbook

.Names("NumInQ").Delete

.Names("TimeInQ").Delete

End With

Worksheets("Reports").Range("NumInQ1").Select

With Selection

For i = 0 To MaxInQ

.Offset(i, 0).Value = i

.Offset(i, 1).Value = TimeInQ(i)

Next

End With

ActiveWorkbook.Names.Add Name:="NumInQ", _



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RefersToR1C1:=Range(Selection, Selection.End(xlDown))

Selection.Offset(0, 1).Select

ActiveWorkbook.Names.Add Name:="TimeInQ", _

RefersToR1C1:=Range(Selection, Selection.End(xlDown))

With Application

.Calculation = xlAutomatic

.MaxChange = 0.001

.CalculateBeforeSave = False

End With

End Sub

Sub UpdateAreas()

Dim TimeSinceLastEvent As Single

TimeSinceLastEvent = Time - TimeLastEvent

TimeLastEvent = Time

TimeInQ(NumInQ) = TimeInQ(NumInQ) + TimeSinceLastEvent

AreaNumInQ = AreaNumInQ + NumInQ * TimeSinceLastEvent

AvgNumInQ = AreaNumInQ / TimeAreaUtil = AreaUtil + NumBusy * TimeSinceLastEvent

End Sub

Sub buildreportsheet()

'

' buildreportsheet Macro

' Macro recorded 05/10/1999 by Shivan Mohd

'

'

Application.DisplayAlerts = False

Sheets("Reports2").DeleteApplication.DisplayAlerts = True

Sheets("Table2").Select

Sheets("Table2").Copy Before:=Sheets(7)

Sheets("Table2 (2)").Select

Sheets("Table2 (2)").Name = "Reports2"

Columns("D:D").Select

Selection.Insert Shift:=xlToRight

Columns("F:F").Select

Selection.Cut Destination:=Columns("D:D")


Selection.Delete Shift:=xlToLeft

Columns("G:G").Select

Selection.Insert Shift:=xlToRightActiveWindow.SmallScroll ToRight:=1

Columns("N:N").Select

Selection.Cut Destination:=Columns("G:G")

Columns("N:N").Select

Selection.Delete Shift:=xlToLeft

ActiveWindow.SmallScroll ToRight:=-7

Columns("B:B").Select


Range("B2").Select

ActiveCell.FormulaR1C1 = "Interarrival Time"

With ActiveCell.Characters(Start:=1, Length:=17).Font

.Name = "Arial"

.FontStyle = "Bold"

.Size = 10



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.Strikethrough = False

.Superscript = False

.Subscript = False

.OutlineFont = False

.Shadow = False

.Underline = xlUnderlineStyleNone

.ColorIndex = 2End With

Columns("B:B").Select

Selection.ColumnWidth = 10.71

Selection.NumberFormat = "0.0000"

Range("B3").Select

ActiveCell.FormulaR1C1 = "=RC[1]"

Dim stepdown As Single

stepdown = 0

Do Until stepdown = NumCusts - 1

Worksheets("Reports2").Cells(4 + stepdown, 2).Value = Worksheets("Reports2").Cells(4 + stepdown,

3).Value - Worksheets("Reports2").Cells(4 - 1 + stepdown, 3).Value

stepdown = stepdown + 1

Loop



Range("F2").Select

ActiveCell.FormulaR1C1 = "Duration Of Service"

With ActiveCell.Characters(Start:=1, Length:=19).Font

.Name = "Arial"

.FontStyle = "Bold"

.Size = 9

.Strikethrough = False

.Superscript = False.Subscript = False

.OutlineFont = False

.Shadow = False

.Underline = xlUnderlineStyleNone

.ColorIndex = 2

End With

stepdown = 0

Do Until stepdown = NumCusts - 1

Worksheets("Reports2").Cells(3 + stepdown, 6).Value = Worksheets("Reports2").Cells(3 + stepdown,

7).Value - Worksheets("Reports2").Cells(3 + stepdown, 4).Value

stepdown = stepdown + 1

LoopSheets("Summary").Select

Range("B3").Select

ActiveCell.FormulaR1C1 = "=AVERAGE(Reports2!RC[4]:R[3333]C[4])"

Range("B2:B6").Select

Selection.NumberFormat = "0.0000"

End Sub

Sub queuelength()

Worksheets("Table2").Select

Dim q, stepup, stepdown As Single

q = 1



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stepup = 1

stepdown = 0

Worksheets("Table2").Cells(3, 2).Select

Do Until Worksheets("Table2").Cells(3 + stepdown, 1).Value = Nextcust - 1

If Worksheets("Table2").Cells(3 +

Mohd Queueing 1999

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