Time-Dependent Analysis of Waiting and Service Time Behaviour in Discrete Time Queue

Abstract

In our daily life we generally find a long queue at the Automated Teller Machine[ATM]. As a result of this a customer has to spend considerable amount of time in queue. In such a situation if instead of using a single ATM machine if we use double ATM machine than it will decrease the waiting time in queue. Against this background, the queuing process is employed with interarrival time and service time. The data for this study was collected from primary source and is limited to ATM service point of a standard Bank where the data collected incorporate the attributes of queuing on the number of customers for four weeks. Eight ATMs at a steady service rate of 0.18 customers per minute is found to be optimal and the waiting time are found to be relatively higher during the hours of 09:00am to 12:00 noon. The research thus reveals that queue exist although its theory is applicable in finding optimal service levels, waiting time might still be lengthy because of some factors. We then derive the arrival rate, service rate, utilization rate, waiting time in the queue and the average number of customers in the queue based on the data Service unavailability was observed to be a contributory factor to queue formation at the ATM point. The queuing process employed with interarrival time and service time do not follow exponential distribution hence, in reducing queue problem, high routine maintenance regime should be actively implemented, backup-staffs could be engaged during peak periods to handle any additional demand instead of the alternative of installing the rather capital-intensive ATM which might be of less utility for most business hours. Queue management should also be made an active part of the bank’s overall strategic queue management processes.

Keywords: Queuing Theory, Waiting Time, Service Rate, Arrival Rate, ATM, Optimal Service Level