WAITING LINE DISTRIBUTION FOR A SYSTEM WITH RANDOM DISRUPTION OF SERVICE

Abstract

Waiting line is a critical part of service industry. It deals with the issues of handling customers and how services are delivered to them. The obvious implication of customers waiting in long and winding queues includes prolonged discomfort and economic lost to them. However, increasing the service rate will require additional number of tellers which implies extra cost to management. Delay occurs in banks when large number of customers was serviced by few tellers. Occasionally, though this may not always be the case, the service system may experience sudden and temporary breakdown like internet or power failure. These are considered rare events and they lead to outliers in the service time data. In this research, Negative Binomial and Generalized-Exponential Distribution were applied to take care of such delays which occur rarely. Data for the study was collected at Guaranty Trust Bank at Masha Lagos for one week through observations and was formulated as multi-server single line queuing model. A total of 193 customers were observed for five working days. The data was analyzed using R Software. It was discovered that on the average 43 customers were found always in the bank, customers are expected to spend 14 minutes in the bank, 28% of the time the system is idle and 72% of the time the system is busy. The results of the analysis showed that using Negative Binomial-Exponential Distribution provides a better fit for the service time than the Exponential distribution