On a Customer-Induced Interruption in a Service System

Abstract

Server induced interruptions such as server break downs, server attending a high priority customer, and server taking a vacation in queues have been extensively studied in the literature. However, customer-induced interruptions such as customers leaving in the middle of a service due to not having enough information for completing a service and customer breakdowns have not been studied so far. The purpose of this work is to introduce customer interruptions in queueing systems. We consider an infinite capacity queueing system with a single server to which customers arrive according to a Poisson process and the service time follows an exponential distribution. The customer interruption while in service occurs according to a Poisson process and the interruption duration follows an exponential distribution. The self-interrupted customers will enter into a finite buffer of size K. Any interrupted customer, finding the buffer full, is considered lost. Those interrupted customers who complete their interruptions will be placed into another buffer of same size. The interrupted customers waiting for service are given non-preemptive priority over new customers. We investigate the behavior of this queuing system. Several performance measures are evaluated. Numerical illustrations of the system behavior are also provided. An optimization problem of interest will be discussed through an illustrative example.