Simulation of a Bank Queue

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Contents
Problem Definition and Goals3
About the Bank3
Logical Model4
Data Gathering and Analysis6
Arena Model Implementation18
Step by Step implementation18
Time Logic18
Cutoff Logic18
Verification and Validation19
Prediction Function / Conclusion23
Appendices27
Appendix 1 : side Results27

Problem Definition and Goals

The purpose of this simulation to obtain important parameters of a bank queue, including bank information, queue length, waiting time in queue and expected wait time of customers in a bank. To obtain the appropriate function for predicting the queue waiting time we need a large numbers of observations. To obtain this data without the need to collect them directly, we simulate the bank work flow and after ensuring that the model built reflects the actual situation, we use the output data and simulations for prediction function. About the Bank

Since the data we received from Bank of America were not given to us as scheduled, we used data from another banking source which is the largest bank owned by private sector in Iran, the bank is called Persian Bank and has been using queue management system to manage its customers’ queue for more than 5 years. For data we needed, we both used data base from the queue management system and some observations that have been done by some individuals. There are different services offered in each branch and by discussion and observing different types of services we divided the offered services to four groups: * Deposits and Withdrawals

* Cashier’s cheque
* Opening a new account
* Multi-Service
The bank has an automatic machine that customers go to, the device gives them a ticket that shows the total numbers of people in the queue, customer’s place in the queue and approximate waiting time.

Logical Model

As was explained customers go to the ticketing machine as soon as they enter the bank, get their tickets, go sit in the shared queue we have and after being called by the system, they go to the servers and receive service. The following is the algorithm we are using to simulate this system. In the real life system, customers are called by the system in our simulated system as soon as a teller is idle the customer goes and sits at it, in which there is no difference between these two models in the matter of queuing theory.

The only attribute of customers are their service type and arrival time which are saved with them during the entrance.

Data Gathering and Analysis
The automated ticketing system saves the arrival time of customers in an access file and the type of service of each customer is determined by the teller and is saved in the same access file. We start our project by determining the distribution of customer arrivals in different hours of the day and different days and then we determine the distribution of service time for the customers. Monthly Distribution of Customer Arrivals:

As said the information about customer Arrivals are saved in an access database file and because of high number of customers we use input analyzer to get the best distribution that fits the arrival times in each month. Here is a summary of the results: p-value| Distribution| Half| Month|

0.66| -0.5 + LOGN(4.71, 6.16)| -| October|
0.17| -0.5 + LOGN(4.54, 7.08)| -| November|
0.75| -0.5 + EXPO(3.63)| First| December|
0.61| -0.5 + LOGN(4.19, 5.66)| Second| December|
0.64| -0.5 + WEIB(6.12, 0.787)| -| January|
0.73| -0.5 + LOGN(5.6, 7.39)| -| February|
0.75| -0.5 + EXPO(4.96)| -| March|
0.56| -0.5 + LOGN(4.04, 5.27)| -| April|

To show that the distribution of service time is not different in different days and the branch being crowded or not does not affect the distribution of service time we use the Kruskal Wallis test. We choose two different days and do the test:

Kruskal-Wallis Test: service time versus day

Kruskal-Wallis Test on service time

day N...
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