Decomposing the queue length distribution of processor-sharing models into queue lengths of permanent customer queues

  • Authors:

  • Sing-Kong Cheung;Hans van den Berg;Richard J. Boucherie

  • Affiliations:

  • University of Twente, Department of Applied Mathematics, Stochastic Operations Research Group, P.O. Box 217, 7500 AE Enschede, The Netherlands;TNO Information and Communication Technology, P.O. Box 5050, 2600 GB Delft, The Netherlands and University of Twente, Department of Computer Science, Design and Analysis of Communication Systems, ...;University of Twente, Department of Applied Mathematics, Stochastic Operations Research Group, P.O. Box 217, 7500 AE Enschede, The Netherlands

  • Venue:
  • Performance Evaluation - Performance 2005
  • Year:
  • 2005

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Abstract

We obtain a decomposition result for the steady state queue length distribution in egalitarian processor-sharing (PS) models. In particular, for multi-class egalitarian PS queues, we show that the marginal queue length distribution for each class equals the queue length distribution of an equivalent single class PS model with a random number of permanent customers. Similarly, the mean sojourn time (conditioned on the initial service requirement) for each class can be obtained by conditioning on the number of permanent customers. The decomposition result implies linear relations between the marginal queue length probabilities, which also hold for other PS models such as the egalitarian PS models with state-dependent system capacity that only depends on the total number of customers in the system. Based on the exact decomposition result for egalitarian PS queues, we propose a similar decomposition for discriminatory processor-sharing (DPS) models, and numerically show that the approximation is accurate for moderate differences in service weights.