Abstract
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 W i ,H i and F i , 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.
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Hirayama, T., Hong, S.J. & Krunz, M.M. A New Approach to Analysis of Polling Systems. Queueing Systems 48, 135–158 (2004). https://doi.org/10.1023/B:QUES.0000039891.78286.dd
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DOI: https://doi.org/10.1023/B:QUES.0000039891.78286.dd