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Approximate Analysis of Queues in Series with Phase-Type Service Times and Blocking

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  • Tayfur Altiok

    (Rutgers University, Piscataway, New Jersey)

Abstract

Queues in series with phase-type service times and finite queue capacities are considered. Servers may get blocked due to the limited space in queues. An approximation method is developed to compute the steady state probability distributions of the number of units in each queue. Three cases are considered: the first queue has an infinite capacity; the first queue has a finite capacity; and the first server is always busy. The method decomposes the system of tandem queues into individual queues with revised arrival and service processes and with queue capacities. Then, each queue is analyzed in isolation within an iterative scheme which relates these queues to each other. The approximation method is computationally efficient and it appears to have an acceptable error level.

Suggested Citation

  • Tayfur Altiok, 1989. "Approximate Analysis of Queues in Series with Phase-Type Service Times and Blocking," Operations Research, INFORMS, vol. 37(4), pages 601-610, August.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:4:p:601-610
    DOI: 10.1287/opre.37.4.601
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    Cited by:

    1. Kozlowski, Dawid & Worthington, Dave, 2015. "Use of queue modelling in the analysis of elective patient treatment governed by a maximum waiting time policy," European Journal of Operational Research, Elsevier, vol. 244(1), pages 331-338.
    2. Berkley, Blair J., 1996. "Analyzing service blueprints using phase distributions," European Journal of Operational Research, Elsevier, vol. 88(1), pages 152-164, January.
    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. 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. Remco Bierbooms & Ivo Adan & Marcel Vuuren, 2013. "Approximate analysis of single-server tandem queues with finite buffers," Annals of Operations Research, Springer, vol. 209(1), pages 67-84, October.
    6. 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.
    7. Asaduzzaman, Md & Chaussalet, Thierry J., 2014. "Capacity planning of a perinatal network with generalised loss network model with overflow," European Journal of Operational Research, Elsevier, vol. 232(1), pages 178-185.
    8. 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.
    9. 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.
    10. Yang, Taho & Lee, Rong-Shean & Chen, Mu-Chen & Chen, Pangwei, 2005. "Queueing network model for a single-operator machine interference problem with external operations," European Journal of Operational Research, Elsevier, vol. 167(1), pages 163-178, November.
    11. Tuǧrul Dayar & Akın Meriç, 2008. "Kronecker representation and decompositional analysis of closed queueing networks with phase-type service distributions and arbitrary buffer sizes," Annals of Operations Research, Springer, vol. 164(1), pages 193-210, November.
    12. 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.
    13. 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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