MONTE CARLOS METHOD OF SIMULATION OF INTER-ARRIVAL AND SERVICE TIME OF USERS OF ATM IN FIRST BANK PLC, AFIKPO BRANCH

CHAPTER ONE

1.0 INTRODUCTION

Simulation is a representation of reality through the use of a model or other device which will react in the same manner as reality under a given set of condition.

According to Donald G. Malcolm, (1953) he define simulated model as one which depict the working of large scale system of men, machine, material and information operating over a period of time in a simulated environment of the actual real world condition. According to Shannon (1954), Simulation is the process of designing a model of real system by conducting experiments with this model for the purpose of understanding the behavior of the operation of the system. In probability theory, simulation means numerical construction of sample of random process.

Monte Carlo simulation is a computerized mathematical technique. In this we need to generate random number to obtain random observation from probability distribution and it’s a sequence of number whose probability of occurrence is the same as that of any other in the sequence. We need random phenomenon in waiting line model, the arrival rate and service rate usually probabilistic rather than deterministic.

In this study, methodology “simulating ATMs” is proposed in order to maximize efficiency of banks to improve their customer’s service and increasing long term relationship with their customers and also reduce the congestion at the ATM center during working hours. The process will show how much time a customer spends and gives suggestion whether a new ATM is required or with the same resource the performance can improve. The research will support the banks in term of decision making for reducing the waiting time of customer by showing a simulation with the help of Monte Carlo method of simulation.

In conclusion simulation is a way of modeling random events such that simulated outcomes closely match real world outcomes. By observing simulated outcome, researcher gain insight on the real world.

Random number are useful for a variety of purpose such as generating data, encryption keys, simulating and modeling complex phenomena and for selecting random samples from the lager data sets. In carrying out Monte Carol simulation, one needs to generate random number to obtain random observation from a probability distribution.

There are many types of random numbers:

A random number is number in sequence whose probability of occurrence is the same as that of any other numbers in the sequence.

1.2 STATEMENT OF PROBLEM

One of the problems the Automatic Teller Machine (ATM) at First Bank is facing is the waiting of customer in the queue for more duration. Mainly the objectives of ATM machines for bank is to keep away the customer from coming to bank and make the process easy for them to avoid the basic procedure they do in bank. But as stated the problem which most ATM face is the long queue in front but then when the problem is only for short while as rest of the time ATM remain idle means adding to operating cost.

The problem is to determine whether more machine are required to be installed to give comfort to customer which is really of short period of time

1.3 SIGNIFICANCE OF THE STUDY

In this study it will help both the researcher and branch manager of First Bank Afikpo to know how customer behave when they meet a long queue and their reaction in the queue and also know the awaiting time of customer in a queue. This research work will provide a robust problem solving technique for the real – world, make a decision related to reducing the ATM queuing problem and to reduce operating cost.

1.4 SCOPE OF THE STUDY

This research is limited to First Bank Plc Afikpo Branch ATM to record the inter – arrival and service time of customer in the ATM point. The data collected was a primary data where more inspector or enumerator were employed and trained for easy collection of data for a period of 5 working days .

1.5 LIMITATION OF THE STUDY

This research posed some challenges especially in data collection. It was quite expensive and time consuming in employing/trainting some inspector in order to assist in collecting the inter arrival and service time of customer in First Bank Plc Afikpo Branch ATM.

Also the problem of reneging and balking of customer posed a serious problem due to impatient of some customer to wait or join a long queue.

The constant visit to First Bank Afikpo Branch for 5 days (4 hours each day) posed serious challenges due to transportation cost and constant visit to internet to make sure this research comes out successfully.

1.6 DEFINITION OF TERMS

Behavior of Arrivals

Service Process or Mechanism

A service mechanism is the manner in which customers are served and leave the service system in series, parallel or mixed.

Service Time Distribution

A time taken by a server from the beginning of a service and the completion of service for the customer is known as the service time.

Multiple server queue model

Exponential service – unlimited queue

In this case, there are multiple but identical servers in parallel that provide service to customers. One queue line is formed and customers are served on the first come, first serve (FCFS). The service time are exponentially distributed.

If there are n customers in the queue system, at any point in time, then the following two cases may be observed:

Case I: where n < S {the numbers of customers in the system is less than the number of servers} then there will be no queue. That is S – n servers will not be busy.

Case II: where n > S (the number of customers in the system is greater than or equal to the number of servers) then all the servers will be busy and the maximum number in the queue will be (n – S).

1. Real random number uses a physical source of randomness
2. Pseudo random number, deterministic sequence that passes test of randomness
3. Quasi random number, low discrepancy.

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