Supplementary variable method applied to the MAP/G/1 queueing system

Bong Dae Choi · Gang Uk Hwang · Dong Hwan Han

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

Abstract In this paper we consider the MAP/G/1 queueing system with infinite capacity. In analysis, we use the supplementary variable method to derive the double transform of the queue length and the remaining service time of the customer in service (if any) in the steady state. As will be shown in this paper, our method is very simple and elegant. As a one-dimensional marginal transform of the double transform, we obtain the generating function of the queue length in the system for the MAP/G/1 queue, which is consistent with the known result.

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References

1984Matrix-Geometric Solutions to Stochastic Models 1991New results on the single server queue with a batch markovian arrival process 1985Matrix-geometric solutions in stochastic models 1990A single-server queue with server vacations and a class of non-renewal arrival processes 1993Queueing analysis: A foundation of performance evaluation, volume 1: Vacation and priority systems, Part 1 1980The N/G/1 queue and its detailed analysis 1989Markov processes whose steady state distribution is matrix-exponential with an application to theGI/PH/1 queue 1994The transient BMAP/G/l queue

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2007Analyzing the finite buffer batch arrival queue under Markovian service process: GI X /MSP/1/N 2008An MAP/G/1 G-queues with preemptive resume and multiple vacations

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