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Reversibility of Tandem Blocking Queueing Systems

Author

Listed:
  • Genji Yamazaki

    (Kogakuin University, Nishi-Shinjuku, Shinjuku-ku, Tokyo 160, Japan)

  • Takeshi Kawashima

    (National Defense Academy, 249 Hashirimizu 1-10-20, Yokosuka, Japan)

  • Hirotaka Sakasegawa

    (Tsukuba University, Sakura, Ibaraki 305, Japan)

Abstract

This paper is concerned with queueing systems of several service stations in series in which each station may consist of multi-servers. An infinite number of customers always waits in front of the first station, and each customer passes through all of the stations in sequence. There is only a finite number of waiting positions between any two adjacent stations. The service time for a customer at any station is assumed to be a random variable, the distribution of which may depend on the station. In this mode of operation the servers at any station will at any time be busy, idle, or blocked. This blocking system is said to be C-reversible if the capacity remains invariant under reversal of the system. The reversed system is obtained by reversing the original stations' order, that is, every customer in the reversed system passes through the original stations in the reverse order. It has already been proved that C-reversibility holds for any blocking system in which each station consists of either a single server of nondeterministic service times or multi-servers of deterministic service times, and that the blocking system has a stronger property than C-reversibility. In this paper we show that two-station blocking systems with multi-server stations of nondeterministic service times are C-reversible, but this property can no longer be extended to three or more station blocking systems with multi-server stations of nondeterministic service times. We also show for the case of multi-server stations of nondeterministic service times that the stronger property which involves invariance of distribution does not hold even for two-station blocking systems.

Suggested Citation

  • Genji Yamazaki & Takeshi Kawashima & Hirotaka Sakasegawa, 1985. "Reversibility of Tandem Blocking Queueing Systems," Management Science, INFORMS, vol. 31(1), pages 78-83, January.
    • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:1:p:78-83
    DOI: 10.1287/mnsc.31.1.78
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    Citations

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    Cited by:

    1. Hyoungtae Kim & Sungsoo Park, 1999. "Optimality of the Symmetric Workload Allocation in a Single-Server Flow Line System," Management Science, INFORMS, vol. 45(3), pages 449-451, March.
    2. Kirkavak, Nureddin & Dincer, Cemal, 1999. "The general behavior of pull production systems: The allocation problems," European Journal of Operational Research, Elsevier, vol. 119(2), pages 479-494, December.
    3. Wai Ki Ching, 2001. "Markovian approximation for manufacturing systems of unreliable machines in tandem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(1), pages 65-78, February.
    4. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    5. Hillier, Frederick S. & So, Kut C., 1996. "On the robustness of the bowl phenomenon," European Journal of Operational Research, Elsevier, vol. 89(3), pages 496-515, March.
    6. Nakade, Koichi, 2000. "New bounds for expected cycle times in tandem queues with blocking," European Journal of Operational Research, Elsevier, vol. 125(1), pages 84-92, August.

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