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Delay Analysis of a Queue with General Service Demands and Phase-Type Service Capacities

  • Michiel De Muynck
  • Herwig Bruneel
  • Sabine Wittevrongel
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 383)

Abstract

We present the analysis of a non-classical discrete-time queueing model where customers demand variable amounts of work from a server that is able to perform this work at a varying rate. The service demands of the customers are integer numbers of work units. They are assumed to be independent and identically distributed (i.i.d.). The service capacities, i.e., the numbers of work units that the server can process in the consecutive slots, are also assumed to be i.i.d. and have a rational probability generating function (pgf). Finally, the numbers of customer arrivals in each slot are i.i.d. as well. We analyze this model analytically using contour integration. Our main result is an expression for the pgf of the customer delay in steady state, from which expressions for the moments of the delay can be derived.

Keywords

Discrete-time queueing theory Service demands Service capacities Complex contour integration 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Michiel De Muynck
    • 1
  • Herwig Bruneel
    • 1
  • Sabine Wittevrongel
    • 1
  1. 1.Department of Telecommunications and Information Processing, Stochastic Modeling and Analysis of Communication Systems Research GroupGhent UniversityGhentBelgium

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