Measurement and performance of the strong stability method

Djamil Aı̈ssani

15 citations0/0 files storedTheory of Probability and Mathematical Statistics

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

Abstract

The aim of this paper is to show how to use in practice the strong stability method and also to prove its efficiency.That is why we chose the GI/M/1 model for which there exist analytical results.For this purpose, we first determine the approximation conditions of the characteristics of the GI/M/1 system.Under these conditions, we obtain the stability inequalities of the stationary distribution of the queue size.We finally elaborate upon an algorithm for the approximation of the GI/M/1 system by the M/M/1 system, which calculates the approximation error with an exact computation.In order to give some idea about its application in practice, we give a numerical example.The accuracy of the approach is evaluated by comparison with some known exact results.

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References

1987Introduction to Queueing Networks 2018Introduction to Queueing Networks 1989The problem of stability in queueing theory

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2008Kernel density in the study of the strong stability of the queueing system 2009Strong stability of the embedded Markov chain in an GI/M/1 queue with negative customers

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