Matrix?geometric analysis of the discrete time Gi/G/1 system

Attahiru Sule Alfa · Wei Li

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

Abstract

In this paper, we show that the discrete GI/G/1 system can be analysed as a QBD process with infinite blocks. Most importantly, we show that Matrix–geometric method can be used for analyzing this general queue system including establishing its stability criterion and for obtaining the explicit stationary probability and the waiting time distributions. This also settles the unwritten myth that Matrix–geometric method is limited to cases with at least one Markov based characterizing parameter, i.e. either interarrival or service times, in the case of queueing systems.

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References

1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1984Matrix-Geometric Solutions to Stochastic Models 1982Operator-geometric stationary distributions for markov chains, with application to queueing models 1969A SINGLE SERVER QUEUE IN DISCRETE TIME.1989A Moment-Iteration Method for Approximating the Waiting-Time Characteristics of the GI/G/1 Queue 1982A Class of Approximations for the Waiting Time Distribution in aGI/G/1 Queueing System

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2003Combined Elapsed Time and Matrix-Analytic Method for the Discrete Time GI/G/1 and GI X /G/1 Systems

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