A New Approach to Analysis of Polling Systems

In this paper, we consider polling systems with J stations with Poisson arrivals and general service distributions attended by a cyclic server. The service discipline at each station is either exhaustive or gated. We propose a new approach to analysis of the mean waiting times in the polling systems...

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Bibliographic Details
Published in:Queueing systems 2004-09, Vol.48 (1/2), p.135-158
Main Authors: Hirayama, Tetsuji, Hong, Sung Jo, Krunz, Marwan M.
Format: Article
Language:English
Subjects:
Algorithms
Customer services
Linear equations
Queuing theory
Studies
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Summary:In this paper, we consider polling systems with J stations with Poisson arrivals and general service distributions attended by a cyclic server. The service discipline at each station is either exhaustive or gated. We propose a new approach to analysis of the mean waiting times in the polling systems. The outline of our method is as follows. We first define the stochastic process Q that represents an evolution of the system state, and define three types of the performance measures Wi,Hi and Fi, which are the expected waiting times conditioned on the system state. Then from the analysis of customers at polling instants, we find their linear functional expressions. The steady state average waiting times can be derived from the performance measures by simple limiting procedures. Their actual values can be obtained by solving J(J+1) linear equations. [PUBLICATION ABSTRACT]
ISSN:0257-0130
1572-9443
DOI:10.1023/B:QUES.0000039891.78286.dd