Analysis of BMAP/MSP/1 queue with MAP generated negative customers and disasters. Issue 12 (18th June 2023)

• Record Type: Journal Article
• Authors: Kumar, Nitin; Gupta, U. C.
• Is Part Of: Communications in statistics. Volume 52:Issue 12(2023)
• Page Start: 4283
• Page End: 4309
• Publication Date: 2023-06-18
• Subjects: Batch Markovian arrival process -- disaster -- G-queue -- markovian service process -- negative customers -- vector generating function; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2021.1990953
• Languages: English
• ISSNs: 0361-0926

Abstract

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.