Modeling scheduling of customers in a bank queue using residual time based Preemptive Priority Queuing

Abstract

In a bank, tellers are usually reserved for different kinds of customers, that is standard customers who carry out the normal deposits/withdraws and corporate customers such as western union and corporate customers. Standard customers are usually very many hence their queues are long while the queue for corporate customers is usually almost always empty because they are few. To reduce on the queuing delay for standard customers without de grading that of the corporate customers, we propose a threshold based preemptive priority scheme where the teller reserved for corporate customers be allowed to serve standard customers but once the corporate customer comes, the service of the standard customer be paused. Pausing of the service of the standard customer depends on the amount of service time remaining for him or her to complete (also called residual service time). From our case study of a bank, we derived expressions for the average sojourn time that we used in the subsequent analysis. Average sojourn time is the total time spent by a customer in the queue and service. From the analytical results, we obtained the optimal threshold for the residual time to be 3 minutes and used it in the subsequent analysis. We observe that standard customers experience lower average sojourn time under preemption with threshold compared to under preemption without threshold regardless of the arrival rate and service rate of customers into the system. On the other hand, corporate customers are observed to experience higher average sojourn time under preemption with threshold than under preemption without threshold. We also observe that the gain experienced by standard customers due to the use of the residual time-based threshold is less than the degradation experienced by corporate customers. Therefore, using residual time-based threshold for preemption greatly improves the performance of standard customers with appreciable service degradation to corporate customers.