Performance Analysis of Queueing Systems with a Particular Service Interruption Discipline

Abstract

In recent years, queueing models with service interruption have been studied extensively due to their widespread applications. This paper is devoted to the study of an M/M/1 queue with a particular service interruption discipline under two types of the maintenance activities, namely the reactive maintenance and the planned maintenance. In the process of serving customers, when the system receives a negative feedback from customers, and in the next N customers to be served, if a negative feedback from the next N customers is received again, the service is interrupted and a reactive maintenance will be triggered immediately; otherwise, if all of the next certain amount of feedbacks are positive, the system administrator has a reason to believe that the occurrence of the negative feedback is an accidental phenomenon, and the reactive maintenance will not be initiated. By using the matrix analytic approach and spectral expansion method, we derive the steady-state probabilities, which are then used to compute the performance measures of the queueing system. Sensitivity analyses of parameters are included in this work for illustrative purposes, and from the perspective of queueing model, we also show that designing the queue size in terms of the steady-state probabilities is a more reasonable and rational method than the expected queue length.