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Title of Journal: Ann Oper Res

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Abbravation: Annals of Operations Research

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Springer US

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DOI

10.1016/0191-8869(95)00116-n

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1572-9338

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Gated polling with stationary ergodic walking time

Authors: Dieter Fiems Eitan Altman
Publish Date: 2012/02/23
Volume: 198, Issue: 1, Pages: 145-164
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Abstract

We investigate a gated polling system with semilinear feedback and Markovian routing We thereby relax the classical independence assumption on the walking times the walking times constitute a sequence of stationary ergodic random variables It is shown that the dynamics of this polling system can be described by semilinear stochastic recursive equations in a Markovian environment We obtain expressions for the first and second order moments of the workload and queue content at polling instants and for the mean queue content and workload at random instantsWith the stability conditions established we now focus on expressions for the first and second moments of mathbfV 0 conditioned on the state of the Markov chain Y 0 Let hatboldsymbol mu the conditional first moment vector be the block column vector with elements boldsymbol mu itriangleq hbox textsf EmathbfV 0 1Y 0 = i i∈Θ Analogously let hatboldsymbol Omega the conditional second moment matrix be the block column vector with elements boldsymbol Omega itriangleq hbox textsf EmathbfV 0 mathbfV 0 1Y 0 = i i∈Θ The following theorem provides expressions for these vectors

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