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On the sojourn times for many-queue head-of-the-line Processor-sharing systems with permanent customers

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  • Andreas Brandt
  • Manfred Brandt

Abstract

We consider a single server system consisting of e queues with different types of customers (Poisson streams) andk permanent customers. The permanent customers and those at the head of the queues are served in processor-sharing by the service facility (head-of-the-line processor-sharing). The stability condition and a pseudo work conservation law will be given for arbitrary service time distributions; for exponential service times a pseudo conservation law for the mean sojourn tunes can be derived. In case of two queues and exponential service times, the generating function of the stationary occupancy distribution satisfies a functional equation being a Riemann-Hilbert problem which can be reduced to a Dirichlet problem for a circle. The solution yields the mean sojourn times as an elliptic integral, which can be computed numerically very efficiently. In case ofn ≥ 2 a numerical algorithm for computing the performance measures is presented, which is efficient forn ≤ 3. Since forn ≥ 4 an exact analytical or/and numerical treatment is too complex a heuristic approximation for the mean sojourn times of the different types of customers is given, which in case of a (completely) symmetric system is exact. The numerical and simulation results show that, over a wide range of parameters, the approximation works well. Copyright Physica-Verlag 1998

Suggested Citation

  • Andreas Brandt & Manfred Brandt, 1998. "On the sojourn times for many-queue head-of-the-line Processor-sharing systems with permanent customers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(2), pages 181-220, June.
    • Handle: RePEc:spr:mathme:v:47:y:1998:i:2:p:181-220
    DOI: 10.1007/BF01194397
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    References listed on IDEAS

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    1. Seelen, L. P., 1986. "An algorithm for Ph/Ph/c queues," European Journal of Operational Research, Elsevier, vol. 23(1), pages 118-127, January.
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