Analysis of BMAP/MSP/1 queue with MAP generated negative customers and disasters

Abstract

This paper studies an infinite-buffer single server queueing model with negative customers and disasters. The ordinary (positive) customers arrive in the system according to the batch Markovian arrival process and join the queue for service. The negative customer and disaster are characterized by two independent Markovian arrival processes. A negative customer removes the positive customer undergoing service, if any, and a disaster makes the system empty by simultaneously removing all the positive customers present in the system. We obtain the steady-state vector generating function (VGF) of the distribution of the number of positive customers in the system at arbitrary epoch. Further, the inversion of the VGF is carried out using the roots method to obtain the distribution. Moreover, the probability vectors at post-departure and pre-arrival epochs are also obtained. The results obtained throughout the analysis are computationally tractable, as illustrated by few numerical examples. Finally, we discuss the impact of the correlation of the arrival process of negative customers and disasters on the performance of the system through some graphical representations.

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