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An Approximation Method for Tandem Queues with Blocking

Author

Listed:
  • Alexandre Brandwajn

    (University of California, Santa Cruz, California, and Pallas International Corporation, San Jose, California)

  • Yung-Li Lily Jow

    (Amdahl Corporation, Sunnyvale, California)

Abstract

We propose an approximate analysis of open systems of tandem queues with blocking caused by finite buffers between servers. Our approach relies on the use of marginal probability distributions (“state equivalence”) coupled with an approximate evaluation of the conditional probabilities introduced through the equivalence. The method iterates over consecutive pairs of servers using the solution of a two-queue system as a building block. It produces performance measures for individual servers as well as an approximation to joint queue-length probability distributions for pairs of neighboring stations. Experience indicates that the number of iterations required for the method grows moderately with the number of nodes in the network. We give examples to demonstrate the accuracy and the convergence properties of the proposed approximation.

Suggested Citation

  • Alexandre Brandwajn & Yung-Li Lily Jow, 1988. "An Approximation Method for Tandem Queues with Blocking," Operations Research, INFORMS, vol. 36(1), pages 73-83, February.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:1:p:73-83
    DOI: 10.1287/opre.36.1.73
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    Citations

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    Cited by:

    1. Haskose, A. & Kingsman, B. G. & Worthington, D., 2002. "Modelling flow and jobbing shops as a queueing network for workload control," International Journal of Production Economics, Elsevier, vol. 78(3), pages 271-285, August.
    2. Osorio, Carolina & Wang, Carter, 2017. "On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 305-339.
    3. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović, 2018. "Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 15-47, June.
    4. Korporaal, R. & Ridder, A.A.N. & Kloprogge, P. & Dekker, R., 1999. "Capacity planning of prisons in the Netherlands," Econometric Institute Research Papers EI 9909-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Subba Rao, S. & Gunasekaran, A. & Goyal, S. K. & Martikainen, T., 1998. "Waiting line model applications in manufacturing," International Journal of Production Economics, Elsevier, vol. 54(1), pages 1-28, January.
    6. Jean-Sébastien Tancrez, 2020. "A decomposition method for assembly/disassembly systems with blocking and general distributions," Flexible Services and Manufacturing Journal, Springer, vol. 32(2), pages 272-296, June.
    7. 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.
    8. Carolina Osorio & Jana Yamani, 2017. "Analytical and Scalable Analysis of Transient Tandem Markovian Finite Capacity Queueing Networks," Transportation Science, INFORMS, vol. 51(3), pages 823-840, August.
    9. Saied Samiedaluie & Vedat Verter, 2019. "The impact of specialization of hospitals on patient access to care; a queuing analysis with an application to a neurological hospital," Health Care Management Science, Springer, vol. 22(4), pages 709-726, December.
    10. Osorio, Carolina & Bierlaire, Michel, 2009. "An analytic finite capacity queueing network model capturing the propagation of congestion and blocking," European Journal of Operational Research, Elsevier, vol. 196(3), pages 996-1007, August.
    11. Schmidt, Linda C. & Jackman, John, 2000. "Modeling recirculating conveyors with blocking," European Journal of Operational Research, Elsevier, vol. 124(2), pages 422-436, July.

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