Simulation for Bank Teller System

1

Ahmed Al Salih

IT-630-G1703_13TW1

Southern New Hampshire University

Project name: Simulation for Bank Teller System


Subject: Computer Simulation/Modeling 13TW1

IT-630-G1703_13TW1: IT-630-G1703

Ahmed Al Salih [email protected]

mailto:[email protected]

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Ahmed Al Salih

IT-630-G1703_13TW1


Table of Contents Base Model ............................................................................................................................. 3

Background ............................................................................................................................. 3

Objective ................................................................................................................................. 3

Key Performance Measures .................................................................................................... 3

Key Decision Variables .......................................................................................................... 3

Problem statement. .................................................................................................................. 4

System and Simulation Specifications .................................................................................... 4

Conceptual Model/ Object Flow Diagram (OFD) ................................................................ 10

Simulation Implementation ................................................................................................... 13

Alternative model 1............................................................................................................... 15

Model Validation .................................................................................................................. 21

What-if questions .................................................................................................................. 23

Simulation Results ................................................................................................................ 24

Calculate Number of Model Replications............................................................................. 26

Output Analysis .................................................................................................................... 29

Alternative Model 2 ............................................................................................................ 132

The objects design: ............................................................................................................... 32

The logic design .................................................................................................................... 32

Object Flow Diagram (ODF) ................................................................................................ 34

Simulation Implementation ................................................................................................... 35

What-if questions .................................................................................................................. 38

Alternative Model 2 Validation ............................................................................................ 38

Output Analyses .................................................................................................................... 41

Summary report for Alternative model 2 .............................................................................. 42

Group Queue Results Comparison........................................................................................ 43

Statistic by individual object ................................................................................................. 44

Statistic by individual object Results Comparison ............................................................... 48

Cost Benefit Analysis ........................................................................................................... 48

Conclusions and Recommendations ..................................................................................... 50

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Ahmed Al Salih

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Simulate the throughput of a bank teller system

Base Model

Background:

Bank Brach manager want to manage the salary for the tellers the work during the day.

The bank buildings have 4 windows for tellers and he wants us to balance the expense of paying for

teller personnel with customer satisfaction.

Simulation is being used to test concepts for setting up a new bank teller system in operation.

Objective

The objective of this modeling and analysis projects is to investigate how many tellers should be

active in a bank during the course of a typical business day; we want to balance the expense of

paying for teller personnel with customer satisfaction.

Key performance measure:

The time customer wait to be served by Teller

Server work load

Key decision variables:

Number of Teller should be active during the shift according to the collecting data that

descript the following distribution of customer arrival times.

Number of servers that serve The Teller’s Widow.

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Problem statement:

The problem here for that project it’s for manage the number of teller they should be active

during a full business day as well the simulation should not affect the customer satisfactions that mean

the waiting time to long.

System and Simulation Specifications:

In this section describe the system simulation component and the logic parts to simulate the bank

case.

The objects design:

As we got told that the “iterance door” is in one side and the “exit door” in the other side.

1. We create a Source Fixed Resource that have name “Front Door” for generate the

customers as item flow into the bank.

2. And create a Sink Fixed Resource that have name “Exit” for exit door to the customer.

3. Queue to accumulate the flow items (customers) from the source and send the flow items

to the processors “Tellers” and I implement the Queue as a “Reception”

4. I have four Processors they implements the Teller windows, have names :

Teller 1, Teller 2, Teller 3 and Teller 4.

5. Create Queue for each server that collect the request from the teller to the server that

have name “ServerQueue1”, “ServerQueue2”, “ServerQueue3”and“ServerQueue4”

6. Processor the process the customer’s transaction, get the input from the “ServerQueue”,

after it done the process send the item flow (customer) to the sink (Exit door) that have

name “server1”, “server2”, “server3” and “server4”.

The Logic design:

1. We collect the data from the bank for the entry per hour and we got the info bellow

a. Peak AM: 09:00-10:00 - 0.33 customer/minute

b. 10:00 AM - 11:30 - 0.10 customer/minute

c. Peak lunch time: 11:30-1:30 – 0.25 customers/minute

d. 1:30 PM - 4:00 PM - 0.10 customer/minute

e. Peak closing time: 4:00-5:00 – 0.5 customers/minute

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So we create in our system a Global Table called “EntryRates”

That has the information about the people rate to enter to the bank during the day.

Bank business day start from 9:00AM to 5:00PM,

As we see the collected data for the entry it is not hourly so we divide the 8 Hour to 16 sections

of 30 mints to make the simulation more specific calculation and accurately as we see in the

picture bellow:

2. Source inter-arrival time : I used in the simulation :

exponential(0,getlabelnum(current,"PeopleCycle"),1)/**/;

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Location = 0

Scale = getlabelnum(current,"PeopleCycle")

Stream = 1

Her I got the value to the Scale from Label name “PeopleCycle”.

“PeopleCycle” label his value get change from the Global Table “EntryRates” every 30 mint , and

that happen after we set a trigger.

3. Labels : I create two labels :

a. PeopleRate: That shows the people rate per minute such as 0.33 customers per

min.

b. PeopleCycle: That shows the time to release or create item flow (one customer

enter the Bank per amount of time),

4. Triggers

a. OnMessage /**set new rate*/

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treenode current = ownerobject(c);

int timeframe = 1+ msgparam(3);

if(timeframe < 17)

{

setlabelnum(current,"PeopleRate",gettablenum("EntryRates",timeframe,1));

setlabelnum(current,"PeopleCycle",30/(30 * gettablenum("EntryRates",timeframe,1)));

//setlabelnum(current,"PeopleCycle",1/ gettablenum("EntryRates",timeframe,1));

}

else {

setlabelnum(current,"PeopleCycle",0);

setlabelnum(current,"PeopleRate",0);

}

senddelayedmessage(current,30,current,0,0,timeframe);

This trigger responds to get the value from the global table and set the new value to the label.

By get the table using the method:

gettablenum(tablename,rownum,colnum)

gettablenum("EntryRates",timeframe,1))

The timeframe increase by one every time the trigger fire as long as less than 17 : the numbers of

rows from the EntryRates table.

To do the math such if we take the first col and row 1,1 = gave us 0.33 as given from the

collected data that mean it is the rate of people per mint , we set the label of people rate

setlabelnum(current,"PeopleRate",gettablenum("EntryRates",timeframe,1));

and the people cycle PeopleCycle that we do some math if we have the PeopleRate = 0.33

0.33 * 60 = 19.8 customer per 60 mints

But we work per 30 mints so it will be

0.33 * 30 = 9.9 customer per 30 mints

And

30 / 9.9 = 3.03 that mean 1 customer per 3.03 mints

So all that implement in this line

setlabelnum(current,"PeopleCycle",30/(30 * gettablenum("EntryRates",timeframe,1)));

and that trigger will fire every 30 min by using this method

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senddelayedmessage(current,30,current,0,0,timeframe);

The form for that code or method:

senddelayedmessage(toobject,delaytime,fromobject,parameter1,parameter2,parameter3)

This causes the message trigger of the object to fire after a certain delay time

b. OnReset

/**set intial people rate*/


setlabelnum(current,"PeopleRate",gettablenum("EntryRates",1,1));

setlabelnum(current,"PeopleCycle",30 * gettablenum("EntryRates",1,1)); // this is time between arrivals

senddelayedmessage(current,0,current,0,0,0);

If we push the reset bottom in the simulation program this trigger will fire and set the two labels

to the first value from the table.

The four Tellers they have process time = 0

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And I make the flow start with the source to one queue 4 Tellers 4 Queue

4 Server Sink.

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Conceptual Model/ Object Flow Diagram (OFD)

Object flow diagram shows the basic structure and outline of a system in a schematic manner and how the

objects flow through the system.

Various Symbols used in the OFD

This symbol is used to represent the source to create the items in the flow.

This symbol is used to represent the fixed resource in the system.

This symbol is used to represent the process in the system.

This symbol is used to represent the decision rule in the system.

This symbol is used to represent the performance measure in the system.

This symbol is used to define downtimes.

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This symbol is used to show links between the objects that involves information and messages.

This symbol is used to represent the sink. It destroys the items that flow through the model.

The object flow diagram shown below provides a conceptual representation of the Base model.

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Object Flow Diagram

Teller 4

Teller 1

Process time = 0

Teller 2

Teller 3

Reception

Wait Time

QueueServer 2

Wait Time Utilization

Process time = 0

Process time = 0

Process time = 0

Throughput

Utilization

Utilization

Utilization

Cust

omer

Custom

er

Customer

Customer

Customer transaction

Exit

QueueServer1

Wait Time

QueueServer3

Wait Time

QueueServer4

Wait Time

Process time

Server 1

Utilization

Process time

Server 4

Utilization

Process time

Server 2

Utilization

Process time

Server 3

Utilization

Customertransaction

Customertransaction

Customertransaction

Customertransaction

Customertransaction

Customertransaction

Customertransaction

Customertransaction

Time BetweenArrivals

TBD TTR



Custom

er tra

nsact

ion

Service Time

Service Time

Service Time

Service Time

Serv

edcu

stom

er

Served

customer

Wai

ting

cust

omer

tran

sact

ion

TBD TTR

Utilization

TBD TTR

TBD TTR

Utilization

Serv

edcu

stom

er

Waiti

ng custo

mer

transa

ctio

n

TBD TTR

Utilization

TBD TTR

TBD TTR

TBD TTR

Front Door

Operator

Operator

Operator

Operator

References

Below textbook has been used as reference.

Beaverstock, M., Greenwood, A., Lavery, E., & Nordgren, W. (2012). Applied Simulation Modeling and

Analysis Using FlexSim (Third ed.). Oren, Utah: FlexSim Software Products,Inc.

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Simulation Implementation

Simulation Basic Units of Measure

1 grid unit = 1 meters

1 time unit = 1 minute

Simulation model default speed = 4 grid unit/ time unit = 4 meters/minute .

Abbreviations and Acronyms

We have not used any special abbreviations and acronyms in our base model.

Modeling Simplifications/ Assumptions None

Fixed Resources – Basic Properties

Name Description Capacity MTBF/MTTR

Front Door Source used to create the Customers

Reception Queue to distribute the customers to the available

Teller’s windows open 100 none

Teller 1 Processor get the input from the Reception Queue

and send the customer transaction to QueueServer1 1 none







QueueServer1 Queue which is used for arrange the customers

from source to Teller 1 100 none






from source to Teller 4 100 None

Server1 Processor used to process the customer transaction

for Teller1 to Sink 1 normal(100, 10, 1)/10

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for Teller2 to Sink 1 normal(100, 10, 1)/10


for Teller3 to Sink 1

normal(100, 10, 1) /

10


for Teller4 to Sink 1

normal(100, 10, 1) /

10

Exit Sink to terminate the Customers 1 none

Fixed Resources – Operation Details

Name Setup Time Process Time

Teller 1 None 0

Teller 2 None 0

Teller 3 None 0

Teller 4 None 0

Server1 None 10

Server2 None 10

Server3 None 10

Server4 None 10

Visual Tools

Object name Description

Security Visual Tool to record the input customer into the global table and

close the source input at 5:00pm

Time_display Display the time in system starting from 9:00 am Wednesday till

the Bank finish process the last customer

Average time in system Display the Average time of customers in system.

Average Waiting Time Display the Average waiting time in QueueServer1,

QueueServer2, QueueServer3, QueueServer4

Fluid Objects

No fluid objects are used in the model.

Network Node Diagram

No networks are used in the model.

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Alternative model 1

User Interfaces

Simulation operates using standard Flexsim interfaces.

Model Views

A model view of the alternate model 1 is provided below.

Fixed Resources – Basic Properties

Use the same fixed resources that have been used in basic model and same MTTF/MTTR.



Teller 1 None 0

Teller 2 None 0

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Teller 3 None 0

Teller 4 None 0

Server1 None getlabelnum(current,"processServer");

and the label get value from global table







Global Tables

Global tables named “gt_EntryRates” has been used with the percentage for IAT to the customer

per every 30 minuts.

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Global tables named “gt_serverUtilization” has been used to set the server Utilization for every

30 minutes. The sever can get the process speed from that global table.

Global tables named “gt_Output” has been used to account the number of

a- customer input

These values from the Source trigger OnExit

int TotalInput = (getoutput(current) + 1);

settablenum("gt_Output",1,1,TotalInput);

b- customer output

These values from the Sink trigger OnEntry //Get the total number of items leaving the system

double TotalOutput = getinput(current); settablenum("gt_Output",1,2,TotalOutput);

c- Total TIS

These values from the Sink trigger OnEntry

double TotalTIS = 0.0;

//Determine item's time in system

double TIS = time() - getcreationtime(item);

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//Update total time in system

TotalTIS= TotalTIS + TIS;

settablenum("gt_Output",1,4, TotalTIS);

d- Avg TIS

These values from the Sink trigger OnEntry double AvgTIS=TotalTIS/TotalOutput;

settablenum("gt_Output",1,3, AvgTIS);

Time Tables

TT_Teller1,3

It is responsible to close teller 1 and teller 3 windows till 1:00 pm

After 240 minutes

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TT_Teller2,4

Close the teller windows 2 and 4, from 1:00 pm to 4:00 pm

Custom Objects

Security Visual Tool to record the input customer into the global table

and close the source input at 5:00pm

Use a trigger code to open the source and close it at 5:00pm

OnReset

senddelayedmessage(current,0, current, 0,1,0); // Start machine

OnNessage

switch(msgparam(2))

{

case 1:

sendmessage(centerobject(current,1),current,0,1,0); // start message

senddelayedmessage(current,480, current, 0,2,0); //time to send the msg to stop the input into the system.

break;

case 2:

sendmessage(centerobject(current,1),current,0,2,0); // stop message

break;

}

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We get the msgparam(2)) from OnReset to pass it to the switch function to run the case 1

case 1:


senddelayedmessage(current,480, current, 0,2,0); //time to send the msg to stop the input into the system.

case 1

Send message to the source to run the case 1 in Source

case 1: // start mahine

openinput(current);

colorgreen(current);

break;

Here will open the input and set the source color to green

After 480 minutes “at 5:00 pm” will send delay message to case 2

And

Case 2

case 2:

sendmessage(centerobject(current,1),current,0,2,0); // stop message

break;

Will send a message to the source to run the case 2 in Source

case 2: // Stop the input

closeoutput(current);

colorred(current);

break;

and the last will close the input and set the source color to red

Model Validation

Validation Plan

1. Control the number of teller’s windows open during the day.

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2. Increase the server process time during the starting and the rush hour to decrease the customer

waiting time

The actual validation:

1. Time table added to control the open teller windows to reduce the teller employee

expensive “salary”

Time Table :

a. TT_Teller1,3

b. TT_Teller2,4

2. Speed up the processor and control the speed for every 30 minutes.

By creating a label name: processServer

And the Process Time get its value from that label.

double value = getlabelnum(current,"processServer");

and the label get its value from the Global Table:

The server trigger OnReset: /**set start up*/


setlabelnum(current,"processServer",gettablenum("gt_serverUtilization",1,1));


senddelayedmessage(current,30, current,0,0,1);

it is set the first label value from the first column/row from the global table name: gt_serverUtilization

And send a delay message to OnMessage trigger to the same server

The server trigger OnMessage:


/**Control the server speed*/

int stepnum = msgparam(3);

switch(stepnum)

{

case 1:




break;

case 2:



break;

case 3:


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break;

case 4:



break;

case 5:



break;

case 6:



break;

case 7:



break;

case 8:



break;

case 9:



break;

case 10:



break;

case 11:



break;

case 12:



break;

case 13:



break;

case 14:

colorred(current);


break;

default:

msg("Error", "Invalid Case value at Machine");

stop();

}

This long code it’s just a switch that get the parameter from message msgparam(3);

And whatever it have number it will run the Case # and send a delay message after 30

minutes to the next case to set the label value so the server process can use this value to set his

own processing speed.

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What-if questions

What if we add extra server for each teller?

Answers: it will add extra cost and we want to reduce the cost

What if we add extra queue per teller?

Answer: there are no effects because we have zero waiting time per queue for teller

The waiting time always in Server Queue.

Performance metrics of interest

Analysis Questions

Definition of Performance Measures

The average and maximum length of the queues for each customer.

The average wait-time for each server queue.

The average number of customers served per hour (throughput).

The average utilization of a server.

Description of Analysis Process/Methodology

Technical Information

Initial conditions: Queue lines are empty and the server is 10 percent.

Run length and basis: 480 minutes based on one business day of Simulation hours

Number of replications and basis: 1

Length of warm-up period and basis: No warm-up time used.

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Simulation Results

The following results were obtained for 480 minutes run of the simulation. For basic model

Total /

Average

Number of customers served 101

Throughput(customers per hour) 12

Average waiting time in

QueueServer1

4.9


QueueServer2

4.1


QueueServer3

4.4


QueueServer4

4.8

The following results were obtained for 480 minutes run of the simulation. For Alternative model

Total /

Average

Number of customers served 101

Throughput(customers per hour) 12


QueueServer1

1.3


QueueServer2

2.5


QueueServer3

1.7


QueueServer4

1

Input Analysis

We have used exponential statistical distributions for inter arrival times and get the value from

the global table as describe at the beginning of the report

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The processing time for tellers is zero.

The processing times for server is changeable depend on the busy time and the rush hour, it gets

the value from the global table as well and it is changeable if needed.

Output Analyses

Basic model

1. The time that keep the bank open after close the entrance “input source” at 5:00 pm

Average is at 515.01 minutes that mean at 5:35 pm.

That gives us 515 – 480 = 35 late to close the bank.

2. The four tellers are working.

Basic model Summary report

Alternative model

1. The time that keep the bank open after close the entrance “input source” at 5:00 pm

Average is at 480.85 minutes almost at 5:02 pm.

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The Bank will close at 5:02 pm

2. Not all the tellers work in same time only on the last hour “the rush hour” to avoid any

bank closing late and customer late

Alternative model Summary report

Calculate Number of Model Replications

Initial Observations with 10 Replications:

The Performance Measure I used Statistic by group.

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And there is group the include the four server queue

Queue_Server_Grp: is a group that contain

1. QueueServer1

2. QueueServer2

3. QueueServer3

4. QueueServer4

So I can experimental on the Queue group

After we use the Flexsim Experimenter on our model for 10 replications, we got the results

The confidence interval (CI) is the range between (mean- hw) and (mean+ hw).

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Calculations for New Number of Replications

Above to calculate the number of replications we need to reduce the Confidence Interval by

50%.

= [ (tn-1, α/2)*s / (√n) ]

α=0.05

n=10

s=1.25

tn-1, α/2= 2.262

=[(2.262)* 1.25/(√10)]= 2.827/3.162=0.894

Because we needed to reduce the Confidence Interval by 50% =0.89/2 =0.44

=10, =0.894, 0.44

= *[

] = *[

] = 40

In order to reduce the Confidence Interval by 50% we need 40 replications.

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Output Analysis

Observations with 40 Replications for Base Model:

Queue_Server_Grp: is a group that contain

1. QueueServer1

2. QueueServer2

3. QueueServer3

4. QueueServer4

As long we build and collect some statistic using the Dashboard Statistics tool.

After running the Experimenter for 40 replications you can click on the upper tab that called

Dashboard Statistics and choose and statistic you want to view for any replications number you

want that you already build before in the Dashboard.

For example this is the replication number 11 and you can see any replication result you want.

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For more details click Experimentation Report

Or open it manual from the project directory inside directory name “reports” file name:

Queue_Server_Grp_basic.htm

Observations with 40 Replications for Alternative Model:

For Queue_Server_Grp: is a group that contain

1. QueueServer1

2. QueueServer2

3. QueueServer3

4. QueueServer4

Queue_Server_Grp_basic.htm

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Or open it manual from the project directory inside directory name “reports” file name:

Queue_Server_Grp_Alternative.htm

Results Comparison

Model Type

CI - Average Stay Time

Queue_Server_Grp

Base Model 2.89 <3.6 < 4.32

Alternate Model 1.74 <2.13 < 2.53

Based on the above results we noticed that there is no overlap for the CI for the Average stay time in the

group Queue_Server_Grp that include all Server Queue

Queue_Server_Grp_Alternative.htm

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Alternative Model 2

The objects design:

As we got told that the “iterance door” is in one side and the “exit door” in the other side.

1. We create a Source Fixed Resource that have name “Front Door” for generate the

customers as item flow into the bank.

2. And create a Sink Fixed Resource that have name “Exit” for exit door to the customer.

3. 4 Queue to accumulate the flow items (customers) from the source and send the flow

items to the processors “Tellers” and I implement the Queue as a “QueueServer1”,

“QueueServer2”, “QueueServer3” and “QueueServer4”

4. I have four Processors they implements the Teller windows, have names :

Server1, Server2, Server 3 and Server 4.

The Logic design:

1. Source: The IAT use the same data collected that I used to simulate the bank problem

with deferent inter arrival time per time as data collected.

That all in the Source fixed resource “Front Door”.

2. Security: is a virtual tool that respond to

a) Control the open input at 9:00 am / close input at 5:00 pm for the source

By sending a message case 1:


senddelayedmessage(current,480, current, 0,2,0); //time to send the msg to it selfe at 5:00pm

break;

case 2:

// stop message send to the source tpstop the input into the system.

sendmessage(centerobject(current,1),current,0,2,0);

break; b) Record the inference customer’s number to global table.

After send message to open the input in source trigger OnExit start send the number

of iterance to the global table “gt_Output”.

int TotalInput = (getoutput(current) + 1) ;

settablenum("gt_Output",1,1,TotalInput);

3. QueueServer (1,2,3 and 4): open input as a Time Table setting

a) QueueServer1 open input at time 240 after 4 hours at 1:00 pm

b) QueueServer2 open input at time 240 after 4 hours at 1:00 pm

c) QueueServer3 close input at time 240 for 180 minutes = 3 hours

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From 1:00 pm to 4:00pm

d) QueueServer4 close input at time 240 for 180 minutes = 3 hours

From 1:00 pm to 4:00pm

4. Teller (1,2,3and 4): implement as person have process time zero “0”

5. Server (1,2,3 and 4): the processor that process the customer’s transaction and they are

implemented as processor have a shape of Teller disk or Rack for teller embedded with

server to process the transaction.

6. Sink: to terminate the flow items “customer” after finish the work in the model

implement with the “Exit”

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Object Flow Diagram (OFD)

QueueServer 2

Wait Time

Throughput

Custom

er

Customer

Customer

Customer

Customer

Exit

QueueServer1

Wait Time

QueueServer3

Wait Time

QueueServer4

Wait Time

Process time

Server 1

Utilization

Process time

Server 4

Utilization

Process time

Server 2

Utilization

Process time

Server 3

Utilization

Customer

Customer

Customer

Customer

Time BetweenArrivals

TBD TTR Customer

Customer

Custom

er

Service Time

Service Time

Service Time

Service Time

Serv

edcu

sto

mer

Served

customerW

aitin

g cu

stom

er

tran

sact

ion

TBD TTR

Utilization

TBD TTR

TBD TTR

Utilization

Serv

edcu

sto

mer

Wai

ting c

ustom

er

transa

ctio

n

TBD TTR

Utilization

TBD TTR

TBD TTR

TBD TTR

Front Door

Operator

Operator

Operator

Operator

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Simulation Implementation

Simulation Basic Units of Measure

1 grid unit = 1 meters

1 time unit = 1 minute

Normal run speed for system is 4 unit / time

Abbreviations and Acronyms

We have not used any special abbreviations and acronyms in our base model.

Modeling Simplifications/ Assumptions None

Fixed Resources – Alternative Model 2 Properties

Name Description Capacity MTBF/MTTR

Front Door Source used to create the Customers

QueueServer1 Queue which is used for arrange the

customers from source to Teller 1

100 none



100 none



100 none



100 None

Exit Sink to terminate the Customers 1 none

Server1 Processor used to process the customer

transaction for Teller1 to Sink

1 normal(100, 10, 1)/10



1 normal(100, 10, 1)/10



1 normal(100, 10, 1) / 10



1 normal(100, 10, 1) / 10

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Server1 None Speed control =5 if over the Threshold in Queue, do SpeedUp by

multiply by 0.9


multiply by 0.9


multiply by 0.9


multiply by 0.9

Visual Tools


Security Visual Tool to record the input customer into the global table and

close the source input at 5:00pm

Time_display Display the time in system starting from 9:00 am Wednesday till

the Bank finish process the last customer

Average time in system Display the Average time of customers in system.

Average Waiting Time 1 Display the Average waiting time in QueueServer1




OutPerHourT1 Display Output per Time from server 1”Teller’s window 1”




Other visual tools For simulate the bank life style.

Fluid Objects

No fluid objects are used in the model.

Recorders


State of Server 1 Displays process state for server 1




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Flow Node

There are 8 flow nodes to manage the customer walk in and out to the bank that have speed

unit/time we assume the normal walk in bank each 1 meter takes 2 seconds 60 / 3 = 20

The speed of node will be 20 meters/minutes.

The last two flow nodes set next to the Exit door have speed of 40 meters/minutes. Because the

customer will walk half of the speed that walk into the street.

The regular walk in street equal 80 Meters/Minutes but it will reduce more than third in bank or

store.

Reference: http://en.wikipedia.org/wiki/Walking_distance_measure

Global Tables

Added the Global tables named “gt_Operations” has been used assign the Maximum value in

Queue for Threshold if it goes more than that number will increase the process speed

automatically.

User Interfaces

Simulation operates using standard Flexsim interfaces.

Model Views A model view of the alternate model 2 is provided below.

http://en.wikipedia.org/wiki/Walking_distance_measure

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What-if questions

1. In the first Alternative model we make the process change his process speed an fixed

time during the day depend on the collected data and we set the in global table and the

processor use a switch with mutable case to set a deferent number to the label

“processServer” and the process time get its value from that changeable label.

The question what if we got some change by the IAT even if its minor change what we

will do for the waiting time and the process time

2. We have dead time from 1:30 PM - 4:00 PM - 0.10 customer/minute !

Do we really need to keep two teller’s windows open and pay for them ???

Alternative Model 2 Validation 1. Change the strategy of the process time that make it more sensitive depend on the Queue

content, and start compare the queue content with the Threshold value and this value are

predefine in global table name is "gt_Operations”.

This value I initial it to 3 I will explain in details how its work:

The code not in the trigger this time but in the process time

//Obtain base service time

double ServiceTime = 5;

//Obtain the speed up threshold

int Threshold=gettablenum("gt_Operations",1,1);

//Determine current number in queue

int NumberInQueue = content(inobject(current,1));

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//Default values

double SpeedUp = 1.0;


//Test to see if threshold is exceeded

if (NumberInQueue>=Threshold)

{

SpeedUp=0.9;

colorred(current);

}

return ServiceTime*SpeedUp;

a) Set the ServiceTime = 5. double ServiceTime = 5;

b) Second step Obtain the speed up threshold. int Threshold=gettablenum("gt_Operations",1,1);

c) Third step to Determine current number in queue that send the flow item to the

processor. int NumberInQueue = content(inobject(current,1));

d) Initial the speedUp to 1 , that mean no change because we will multiply the

ServiceTime by the SpeedUp and color green ,

Here the color will no change because we import extra shape but I leave as a

reference if we need to go back to original processor shape double SpeedUp = 1.0;


e) Test to see if threshold is exceeded to compare if the number in queue more than the

threshold value or not.

If the condition exist will change the value of the speedup to 0.9 and change the color

to red to indicate that we get overload in this window and we had to change the Speed

value to 0.9 if (NumberInQueue>=Threshold)

{

SpeedUp=0.9;

colorred(current);

}

f) return ServiceTime*SpeedUp;

if it is normal “no load in queue will multiply by 1, if not will multiply by 0.9 to

reduce the Service Time value.

2. From 1:30 PM - 4:00 PM we keep only one teller’s window open and we add some extra

code that when Intuit for over load in queue for teller 1, will push a bottom and call for

assistance from the customer service person to open another teller’s window.

And this rarely happens.

by sending a message with message parameter 1 msgparam(1) = 1 ,= “1,0,0” senddelayedmessage(centerobject(current,1),10, current,1,0,0);

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That will be in the process time code when checking for over load in queue teller 1

if (NumberInQueue>=Threshold)

{

SpeedUp=0.9;

colorred(current);


}

This message will send to the visual tool "Call for assistance"

This virtual tool have code OnMessage if get msgparam(1) = 1 int callassis = msgparam(1);

switch(callassis)

{

case 1:

colorred(current);


break;

Will change the color to the text to red and send a message to QueueServer2 that connect to

central port 2 (centerobject(current,2), to open input the code will be in QueueServer2 OnMessage

that have msgparam(1) = 2 .

The code in QueueServer2 OnMessage:

case 2:

colorgray(current);

openinput(current);

break;

and if everything goes normal and there is not too much in QueueServer1 that mean when

processer “Server1” for Teller have no load and goes back to normal process time with no need

to speed Up will send a message to the virtual tool but will take 10 minute to not interrupt the

customer service teller or the manager that open teller two window. //Default values

double SpeedUp = 1.0;


senddelayedmessage(centerobject(current,1),10, current,2,0,0);

And the virtual tool "Call for assistance" will send a message to QueueServer2 to close

the input after 20 minutes to get the total of 30 minutes the default amount when request

assistance. case 2:


senddelayedmessage(centerobject(current,2),20, current,1,0,0);

break;

The Trigger OnMessage in QueueServer2 will be: case 1:

colorred(current);

stopinput(current);

break;

To set the color back to red and close the input.

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Output Analyses

Simulation Results

The following results were obtained for 480 minutes run of the simulation. For Alternative model 2

Basic

model

Alternative

1

Alternative

2

Number of customers served 101 101 96

Throughput(customers per

hour)

12 12 12


QueueServer1

4.9 1.3 2.85


QueueServer2

4.1 2.5 0.00


QueueServer3

4.4 1.7 1.67


QueueServer4

4.8 1 2.80

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Summary report for Alternative model 2

The summery report for the Alternative model 2 Click here

Or open it manual from the project directory inside directory name “Reports” file name:

summaryreport_Alternative2.csv

Note: the Bank will close in average after 8-10 minutes from closing the entrance door around

5:08 pm. It is acceptable to the customers and employees.

Observations with 40 Replications for Alternative 2 Model:

For Queue_Server_Grp: is a group that contain

1. QueueServer1

2. QueueServer2

3. QueueServer3

4. QueueServer4

Reports/summaryreport_Alternative2%20.csv

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Or open it manual from the project directory inside directory name “Reports” file name:

Queue_Server_Grp_Alternative2.htm

Group Queue Results Comparison

Model Type

CI - Average Stay Time

Queue_Server_Grp

Base Model 2.89 < 3.6 < 4.32

Alternate Model 1 1.74 < 2.13 < 2.53

Alternate Model 2 2.07 < 2.4 < 2.73

Based on the above results we noticed that there is no overlap for the CI for the Average stay time in the

group Queue_Server_Grp that include all Server Queue between the Alternate Model 2 VS Base Model

And we do have overlap between the Alternate Model 1 VS Alternate Model 2. We should take into

consideration the Alternate Model 2 more close to the reality because it has the customer walk time. And

still we have the Cost Benefit Analysis to decide which one will give us more benefit.

The Mean of Base Model = 3.6 Std dev S = 2.21 α = 0.05

The Mean of Alternate Model 1 = 2.13 Std dev S =1.21 P = 0.05

The Mean of Alternate Model 2 = 2.4 Std dev S =1.02

Paired-t is also used quite often in simulation modeling and analysis. It uses the following hypothesis:

H0: µ1 = µ2 → µ1 - µ2 → = 0 → µ12 = 0

H1: µ1 ≠ µ2 → µ1 - µ2 → ≠ 0 → µ12 = 1

If H0 (the null hypothesis) is rejected, then it is concluded that there is a significant difference in the mean of the

two populations that represent the two alternatives.

Hw0 = (tn-1, α/2)*S / (√n) = (t40-1, 0.05/2)* 2.21/( 40) = (t39,0.025)*2.21/(6.32) = 2.0227 * 0.3496 = 0.7071 (X - hw) = 3.6 – 0.7071= 2.8929 (X + hw) = 3.6 + 0.7071 = 4.3071 Therefore, the 95% CI is the range from (2.8929) to (4.3071).

Hw2 = (tn-1, α/2)*S / (√n) = (t40-1, 0.05/2)* 1.02/( 40) = (t39,0.025)*1.02/(6.32) = 2.0227 * 0.1613= 0.3262 (X - hw) = 2.4 – 0.3262 = 2.0738 (X + hw) = 2.4 + 0. 3262 = 2.7262 Therefore, the 95% CI is the range from (2.0738) to (2.7262).

H0 not equal h2 we reject the haypothisis and we accept the alternative model 2

Reports/Queue_Server_Grp_Alternative2.htm

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Statistic by individual object Now will do experimenter for Statistic by individual object for the three models:

Observations with 40 Replications for Basic Model:

1.

Object: "QueueServer1"

Statistic: AverageStaytime

2.



3.



4.



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Observations with 40 Replications for Alternate Model 1:

1.



2.



3.



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4.



Observations with 40 Replications for Alternate Model 2:

1.



2.



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3.



4.



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Statistic by individual object Results Comparison

Model Type QueueServer1 QueueServer2 QueueServer3 QueueServer4

Base Model 2.98 < 3.67 < 4.35 3.02 < 3.67 < 4.32 2.84 < 3.61 < 4.38 2.85 < 3.67 < 4.5

Alternate Model 1 1.33 < 1.91 < 2.49 1.52 < 2.08 < 2.65 1.68 < 2.44 < 3.19 1.57 < 2.11 < 2.64

Alternate Model 2 3.93 < 4.82 < 5.7 0 < 0 < 0 1.85 < 2.46 < 3.07 1.88 < 2.33 < 2.78

Cost Benefit Analysis

First we collect some statistics about the regular bank teller salary in Manchester NH

And we get the average salary is 29.00 $ per hour for each teller.

Reference: http://www.indeed.com/salary?q1=Bank+Teller&l1=manchester+

Cost per basic model calculate

Base Model Cost Benefit Analysis: has 4 teller’s window open for all the business hour per day.

29.00 * 4 = 116 $ per one hour for 4 tellers

116*8 = 928 $ per one day

Alternate Model 1 Model Cost Benefit Analysis:

Two teller’s window opens (Teller2 and Teller 4) from 9:00 am to 1:00 pm = 4 hours

29.00 * 2 = 58$ per one hour for two tellers

http://www.indeed.com/salary?q1=Bank+Teller&l1=manchester

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For first four hours cost will be 232 $

Two teller’s window opens (Teller1 and Teller 3) from 1:00 pm to 5:00 pm = 4 hours

232 $

Plus (Teller2 and Teller 4) will open in the last hour to avoid the busy time in the rush hour

=58$

For the last four hours cost will be 232+58 = 290 $

The cost for one business day 232 $ + 290 $ = 522 $

Alternate Model 2 Model Cost Benefit Analysis:

Two teller’s window opens (Teller3 and Teller 4) from 9:00 am to 1:00 pm = 4 hours

29.00 * 2 = 58$ per one hour for two tellers

For first four hours cost will be 232 $

One teller (Teller1) open from 1:00 pm to 5:00 pm and will keep teller’s window 2 available if

the bank got busy, the Teller1 can call for assistance from the “MOD” manager on duty or the

customer service person and that will don’t add extra charge on the tellers salaries budget.= 116$

Plus the (Teller3 and Teller 4) will open the last hour to make sure they can cover the rush hour.

=58 $

The last four hours cost will be 116 $ + 58 $ = 174

The Total cost for one business day = 232 + 174 = 406 $

From the cost results that we have, will show Cost Benefit Analysis comparison for the three

models.

Cost Benefit Analysis

Base Model Alternate Model 1 Alternate Model 2

Total salary Per week 928*5 = 4,640 $ 2,610 $ 2030 $

Total salary Per month 4,640*4 = 18,560 $ 10,440 $ 8,120 $

Total salary Per year 18,560*12= 222,720 $ 125,280 $ 97,440 $

The bank will save:

222,720 $ – 125,280 $ = 97,440 $ every year by using Alternate Model 1

222,720 $ – 97,440 $ = 125,280 $ every year by using Alternate Model 2

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Conclusions and Recommendations

Alternate Model 2 did not have any balked customers and this model has been found to be the most cost

effective compared to Base Model and Alternate Model 1. There are no customers balked even in the

Alternate Model 1 but this will cost around 1.5 times more to the business compared to the Alternate

Model 2. With respect to the Average stay time in the Queue, Alternate Model 1 has best values

compared to the Base Model and Alternate Model 2. Alternate Model 2 Average Stay times are

significantly better compared to the Base Model. From this analysis we recommend Alternate Model 2 as

the optimum solution.

Simulation for Bank Teller System

Technology

modeling simplifications

standard flexsim

00pm timedisplay

average stay

sink fixed

tellers window

customer service

source fixed