A simple analysis of the batch arrival queue with infinite-buffer and Markovian service process using roots method: $$ GI ^{[X]}/C$$ G I [ X ] / C - $$ MSP /1/\infty $$ M S P / 1 / ∞

M. L. Chaudhry (), A. D. Banik () and A. Pacheco ()
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M. L. Chaudhry: Royal Military College of Canada
A. D. Banik: Indian Institute of Technology
A. Pacheco: Universidade de Lisboa

Annals of Operations Research, 2017, vol. 252, issue 1, No 9, 135-173

Abstract: Abstract We consider a batch arrival infinite-buffer single-server queue with generally distributed inter-batch arrival times with arrivals occurring in batches of random sizes. The service process is correlated and its structure is governed by a Markovian service process in continuous time. The proposed analysis is based on roots of the associated characteristic equation of the vector-generating function of system-length distribution at a pre-arrival epoch. We also obtain the steady-state probability distribution at an arbitrary epoch using the classical argument based on Markov renewal theory. Some important performance measures such as the average number of customers in the system and the mean sojourn time have also been obtained. Later, we have established heavy- and light-traffic approximations as well as an approximation for the tail probabilities at pre-arrival epoch based on one root of the characteristic equation. Numerical results for some cases have been presented to show the effect of model parameters on the performance measures.

Keywords: General independent arrival; Batch arrival; Infinite-buffer; Queue; Continuous time Markovian service process (C-MSP); Roots; Weibull-; Log-normal-; Pareto-inter-batch arrival distribution (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-015-2026-y

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