Efficient Computational Analysis of Stationary Probabilities for the Queueing System BMAP / G /1/ N With or Without Vacation(s)

A. D. Banik () and M. L. Chaudhry ()
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A. D. Banik: School of Basic Sciences, Indian Institute of Technology, Bhubaneswar, Permanent Campus Argul, Jatni, Khurda-752050 Odisha, India
M. L. Chaudhry: Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario, Canada K7K 7B4

INFORMS Journal on Computing, 2017, vol. 29, issue 1, 140-151

Abstract: We consider a finite-buffer single-server queue with batch Markovian arrival process. In the case of finite-buffer batch arrival queue, there are different customer rejection/acceptance strategies such as partial batch rejection, total batch rejection, and total batch acceptance policy. We consider partial batch rejection strategy throughout our paper. We obtain queue length distributions at various epochs such as pre-arrival, arbitrary, and post-departure as well as some important performance measures, like probability of loss for the first, an arbitrary, and the last customer of a batch, mean queue lengths, and mean waiting times. The corresponding queueing model under single and multiple vacation policy has also been investigated. Some numerical results have been presented in the form of tables by considering phase-type and Pareto service time distributions. The proposed analysis is based on the successive substitutions in the Markov chain equations of the queue-length distribution at an embedded post-departure epoch of a customer. We also establish relationships among the queue-length distributions at post-departure, arbitrary, and pre-arrival epochs using the classical argument based on Markov renewal theory and semi-Markov processes. Such queueing systems find applications in the performance evaluation of teletraffic part in 4G A11-IP networks.

Keywords: finite-buffer queue; batch Markovian arrival process; single server; partial batch rejection policy; single- and multiple-vacation policy; Pareto service time distribution (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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