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On Decomposition Methods for Tandem Queueing Networks with Blocking

Author

Listed:
  • Yves Dallery

    (Université Pierre et Marie Curie, Paris, France)

  • Yannick Frein

    (Institut National Polytechnique de Grenoble, Saint Martin d'Hères, France)

Abstract

Queueing networks with blocking are useful for modeling and analyzing discrete event systems, especially manufacturing systems. Most analysis methods for queueing networks with blocking are approximation methods that involve a decomposition of the network into a set of subsystems. This paper presents some insight into these decomposition methods as well as new results. Attention is mainly restricted to the case of tandem queueing networks with exponential service times and blocking-after-service. This type of blocking is especially encountered in manufacturing systems. The first aim of this paper is to improve the understanding and present a unified view of the decomposition methods. We show that decomposition methods can be classified according to three main approaches. One of these approaches is of special interest because it offers a symmetrical view of the decomposition. The second aim of the paper is to provide properties pertaining to these decomposition methods in the case of exponential characterizations of subsystems. We prove the existence and uniqueness of the solution. Moreover, we prove the convergence of the computational algorithm associated with the symmetrical approach.

Suggested Citation

  • Yves Dallery & Yannick Frein, 1993. "On Decomposition Methods for Tandem Queueing Networks with Blocking," Operations Research, INFORMS, vol. 41(2), pages 386-399, April.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:2:p:386-399
    DOI: 10.1287/opre.41.2.386
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    Citations

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    Cited by:

    1. Tan, Baris, 1997. "Variance of the throughput of an N-station production line with no intermediate buffers and time dependent failures," European Journal of Operational Research, Elsevier, vol. 101(3), pages 560-576, September.
    2. Eva K. Lee & Siddhartha Maheshwary & Jacquelyn Mason & William Glisson, 2006. "Large-Scale Dispensing for Emergency Response to Bioterrorism and Infectious-Disease Outbreak," Interfaces, INFORMS, vol. 36(6), pages 591-607, December.
    3. Palmer, Geraint I. & Harper, Paul R. & Knight, Vincent A., 2018. "Modelling deadlock in open restricted queueing networks," European Journal of Operational Research, Elsevier, vol. 266(2), pages 609-621.
    4. Tan, Baris & Yeralan, Sencer, 1996. "A fuzzy decomposition method for multistation production systems subject to blocking," International Journal of Production Economics, Elsevier, vol. 42(3), pages 245-262, April.
    5. Bolat, Ahmet, 1997. "Sequencing jobs for an automated manufacturing module with buffer," European Journal of Operational Research, Elsevier, vol. 96(3), pages 622-635, February.
    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. Tancrez, Jean-Sbastien & Semal, Pierre & Chevalier, Philippe, 2009. "Histogram based bounds and approximations for production lines," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1133-1141, September.
    8. Gregory Dobson & Hsiao-Hui Lee & Arvind Sainathan & Vera Tilson, 2012. "A Queueing Model to Evaluate the Impact of Patient "Batching" on Throughput and Flow Time in a Medical Teaching Facility," Manufacturing & Service Operations Management, INFORMS, vol. 14(4), pages 584-599, October.
    9. Raj, G. & Roy, D. & de Koster, R. & Bansal, V., 2024. "Stochastic modeling of integrated order fulfillment processes with delivery time promise: Order picking, batching, and last-mile delivery," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1114-1128.
    10. 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.
    11. Jean-Sébastien Tancrez & Philippe Chevalier & Pierre Semal, 2011. "Probability masses fitting in the analysis of manufacturing flow lines," Annals of Operations Research, Springer, vol. 182(1), pages 163-191, January.
    12. Michael Manitz, 2015. "Analysis of assembly/disassembly queueing networks with blocking after service and general service times," Annals of Operations Research, Springer, vol. 226(1), pages 417-441, March.
    13. 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.
    14. Papadopoulos, H. T. & Vidalis, M. I., 2001. "Minimizing WIP inventory in reliable production lines," International Journal of Production Economics, Elsevier, vol. 70(2), pages 185-197, March.
    15. Mark Vroblefski & R. Ramesh & Stanley Zionts, 2000. "General Open and Closed Queueing Networks with Blocking: A Unified Framework for Approximation," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 299-316, November.
    16. Elisa Gebennini & Andrea Grassi & Cesare Fantuzzi, 2015. "The two-machine one-buffer continuous time model with restart policy," Annals of Operations Research, Springer, vol. 231(1), pages 33-64, August.
    17. 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.
    18. Eva Lee & Siddhartha Maheshwary & Jacquelyn Mason & William Glisson, 2006. "Decision support system for mass dispensing of medications for infectious disease outbreaks and bioterrorist attacks," Annals of Operations Research, Springer, vol. 148(1), pages 25-53, November.
    19. Osorio, Carolina & Bierlaire, Michel, 2012. "A tractable analytical model for large-scale congested protein synthesis networks," European Journal of Operational Research, Elsevier, vol. 219(3), pages 588-597.

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