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Simulation-based transfer function modeling for transient analysis of general queueing systems


  • Yang, Feng
  • Liu, Jingang


This paper is concerned with characterizing the transient behavior of general queueing systems, which is widely known to be notoriously difficult. The objective is to develop a statistical methodology, integrated with extensive offline simulation and preliminary queueing analysis, for the estimation of a small number of transfer function models (TFMs) that quantify the input–output dynamics of a general queueing system. The input here is the time-varying arrival rate of jobs to the system; the time-dependent output performances include the departure rate of jobs and the mean of the work in process (i.e., number of jobs in the system). The resulting TFMs are difference equations, like the discrete approximations of the ordinary differential equations provided by an analytical approach, while possessing the high fidelity of simulation. Our method is expected to overcome the shortcomings of the existing transient analysis approaches, i.e., the computational burden of simulation and the lack of fidelity of analytical queueing models.

Suggested Citation

  • Yang, Feng & Liu, Jingang, 2012. "Simulation-based transfer function modeling for transient analysis of general queueing systems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 150-166.
  • Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:150-166
    DOI: 10.1016/j.ejor.2012.05.040

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    References listed on IDEAS

    1. Michael H. Rothkopf & Shmuel S. Oren, 1979. "A Closure Approximation for the Nonstationary M/M/s Queue," Management Science, INFORMS, vol. 25(6), pages 522-534, June.
    2. Lawrence M. Leemis, 1991. "Nonparametric Estimation of the Cumulative Intensity Function for a Nonhomogeneous Poisson Process," Management Science, INFORMS, vol. 37(7), pages 886-900, July.
    3. Zapfel, G. & Missbauer, H., 1993. "Production Planning and Control (PPC) systems including load-oriented order release -- Problems and research perspectives," International Journal of Production Economics, Elsevier, vol. 30(1), pages 107-122, July.
    4. Gabriel R. Bitran & Devanath Tirupati, 1988. "Multiproduct Queueing Networks with Deterministic Routing: Decomposition Approach and the Notion of Interference," Management Science, INFORMS, vol. 34(1), pages 75-100, January.
    5. Stephen G. Eick & William A. Massey & Ward Whitt, 1993. "Mt/G/\infty Queues with Sinusoidal Arrival Rates," Management Science, INFORMS, vol. 39(2), pages 241-252, February.
    6. Otis B. Jennings & Avishai Mandelbaum & William A. Massey & Ward Whitt, 1996. "Server Staffing to Meet Time-Varying Demand," Management Science, INFORMS, vol. 42(10), pages 1383-1394, October.
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