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Approximation Analysis of Open Acyclic Exponential Queueing Networks with Blocking

Author

Listed:
  • Hyo-Seong Lee

    (Kyung Hee University, Seoul, Korea)

  • Stephen M. Pollock

    (University of Michigan, Ann Arbor, Michigan)

Abstract

An arbitrary configuration of an open queueing network with exponential service times and finite buffers is analyzed. We offer an iterative procedure for approximating the marginal occupancy probabilities for each queue of the system. The method decomposes the queueing network into individual queues and analyzes each in isolation using information from only its nearest neighbors. Based upon the SIMP approximation previously used for tandem queues, it replaces each server's service time with a clearance time, which includes blocking, and each server's arrival rate by an equivalent acceptance rate. The procedure is easy to implement and requires modest memory and computer time. Extensive numerical experiments, performed for various topologies, yield accurate results compared with those obtained by exact or simulation methods.

Suggested Citation

  • Hyo-Seong Lee & Stephen M. Pollock, 1990. "Approximation Analysis of Open Acyclic Exponential Queueing Networks with Blocking," Operations Research, INFORMS, vol. 38(6), pages 1123-1134, December.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:6:p:1123-1134
    DOI: 10.1287/opre.38.6.1123
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    Cited by:

    1. Lee, Heeseok, 1995. "Assignment of a job load in a distributed system: A multicriteria design method," European Journal of Operational Research, Elsevier, vol. 87(2), pages 274-283, December.
    2. Kerbache, Laoucine & Smith, J. MacGregor, 2000. "Multi-objective routing within large scale facilities using open finite queueing networks," European Journal of Operational Research, Elsevier, vol. 121(1), pages 105-123, February.
    3. 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.
    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. 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.
    7. Hui-Yu Zhang & Qing-Xin Chen & James MacGregor Smith & Ning Mao & Ai-Lin Yu & Zhan-Tao Li, 2017. "Performance analysis of open general queuing networks with blocking and feedback," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5760-5781, October.
    8. 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.

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