Markovian polling systems with mixed service disciplines and retrial customers

Markovian polling systems with mixed service disciplines and retrial customers

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Article ID: iaor2002986
Country: Spain
Volume: 7
Issue: 2
Start Page Number: 305
End Page Number: 322
Publication Date: Jul 1999
Journal: TOP
Authors:
Keywords: retrial queues
Abstract:

A Markovian polling model with a mixture of exhaustive and gated type stations is considered. The customers are of n different types and arrive at the system according to the Poisson distribution, in batches containing customers of all types (correlated batch arrivals). The customers who find upon arrival the server unavailable repeat their arrival individually after a random amount of time (retrial customers). The service times Ti and the switchover times Vij are arbitrarily distributed with different distributions for the different stations. For such a model we obtain formulae for the expected number of customers in each station in a steady state. Our formulae hold also for zero switchover periods and can easily be adapted to hold for the corresponding ordinary Markovian mixed polling models with/without switchover times and correlated batch arrivals. Numerical calculations are finally used to observe system's performance.

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