An Application of Queuing Theory to ATM Service Optimization: A Case Study

Abstract

Unmanaged queues are detrimental to the gainful operation of service systems and results in a lot of other managerial problems. This paper applies queuing theory to determine optimal service level for a case ATM base on a customer-defined criterion of wait time not exceeding eight (8) minutes.  In pursuance of this, the prevailing operation characteristics of the case ATM as a queuing system where defined. Direct non-participatory observation and questionnaire were engaged to record time measurements and primary data. Measurements were taken on arrival times and service times of customers who arrived at the terminal within the hours of 8:00 am to 4:00 pm. The Chi-squared Goodness of Fit test was performed on collected data. This established the interarrival times at the case ATM as exponentially distributed. The M/M/s queuing model therefore best illustrates the ATM queuing system of the case bank. A queuing theory based decision support system was developed as a result and applied to analyse and suggest improvement in waiting time. Two ATMs at a service rate of 0.60 customers per minute is found to be optimal for the case bank albeit waiting time are found to be relatively higher during the hours of 11:00am to 1:00pm and month endings. The research thus reveals that although queuing theory is applicable in finding optimal service levels, waiting time might still be lengthy because of external factors. Service unavailability was observed to be a contributory factor to queue formation at the case ATM. A routine maintenance regime should be actively implemented in curtailing such problems. For short term queue management however, 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