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Approximating nonstationary ph(t)⧸ph(t)⧸1⧸c queueing systems

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  • Ong, Kim L.
  • Taaffe, Michael R.

Abstract

A state space partitioning and surrogate distribution approximation (SDA) approach for analyzing the time-dependent behavior of queueing systems is described for finite-capacity, single server queueing systems with time-dependent phase arrival and service processes. Regardless of the system capacity, c, the approximation requires the numerical solution of only k1 + 3k1k2 differential equations, where k1 is the number of phases in the arrival process and k2 is the number of phases in the service process, compared to the k1 + ck1k2 Kolmogorov-forward equations required for the classic method of solution. Time-dependent approximations of mean and standard deviation of the number of entities in the system are obtained. Empirical test results over a wide range of systems indicate that the approximation is extremely accurate.

Suggested Citation

  • Ong, Kim L. & Taaffe, Michael R., 1988. "Approximating nonstationary ph(t)⧸ph(t)⧸1⧸c queueing systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(5), pages 441-452.
    • Handle: RePEc:eee:matcom:v:30:y:1988:i:5:p:441-452
    DOI: 10.1016/0378-4754(88)90057-2
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    Cited by:

    1. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.

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