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The Power-Series Algorithm Applied to the Shortest-Queue Model

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  • J. P. C. Blanc

    (Tilburg University, Tilburg, The Netherlands)

Abstract

An iterative numerical technique for the evaluation of queue length distribution is applied to multiserver systems with queues in parallel in which customers join (one of) the shortest queues upon arrival. The technique is based on power-series expansions of the state probabilities as functions of the load of the system. The convergence of the series is accelerated by applying a modified form of the epsilon algorithm. The shortest-queue model lends itself particularly well to a numerical analysis by means of the power-series algorithm due to a specific property of this model. Numerical values for the mean and the standard deviation of the total number of customers and the waiting times in stationary symmetrical systems are obtained for practically all values of the load for systems with up to ten queues and for a load not exceeding 75% for systems with up to 30 queues. Data are also presented for systems with four queues and unequal service rates.

Suggested Citation

  • J. P. C. Blanc, 1992. "The Power-Series Algorithm Applied to the Shortest-Queue Model," Operations Research, INFORMS, vol. 40(1), pages 157-167, February.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:1:p:157-167
    DOI: 10.1287/opre.40.1.157
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    References listed on IDEAS

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    1. Blanc, J.P.C., 1988. "A numerical approach to cyclic-service queueing models," Other publications TiSEM ec3c0bf2-d86f-4ecd-b873-1, Tilburg University, School of Economics and Management.
    2. B. M. Rao & M. J. M. Posner, 1987. "Algorithmic and approximation analyses of the shorter queue model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 381-398, June.
    3. Gertsbakh, Ilya, 1984. "The shorter queue problem: A numerical study using the matrix-geometric solution," European Journal of Operational Research, Elsevier, vol. 15(3), pages 374-381, March.
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    Citations

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    Cited by:

    1. Partha Chakroborty & Rahul Gill & Pranamesh Chakraborty, 2016. "Analysing queueing at toll plazas using a coupled, multiple-queue, queueing system model: application to toll plaza design," Transportation Planning and Technology, Taylor & Francis Journals, vol. 39(7), pages 675-692, October.
    2. Blanc, J.P.C., 1990. "Performance evaluation of polling systems by means of the power-series algorithm," Research Memorandum FEW 459, Tilburg University, School of Economics and Management.
    3. Danielle Tibi, 2019. "Martingales and buffer overflow for the symmetric shortest queue model," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 153-190, October.
    4. Blanc, J.P.C., 2009. "Bad luck when joining the shortest queue," European Journal of Operational Research, Elsevier, vol. 195(1), pages 167-173, May.
    5. Plinio S. Dester & Christine Fricker & Danielle Tibi, 2017. "Stationary analysis of the shortest queue problem," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 211-243, December.
    6. van den Hout, W.B. & Blanc, J.P.C., 1994. "The power-series algorithm for Markovian queueing networks," Discussion Paper 1994-67, Tilburg University, Center for Economic Research.
    7. van den Hout, W.B. & Blanc, J.P.C., 1994. "The Power-Series Algorithm for a Wide Class of Markov Processes," Discussion Paper 1994-87, Tilburg University, Center for Economic Research.
    8. P. Patrick Wang, 2000. "Workload distribution of discrete‐time parallel queues with two servers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 440-454, August.
    9. M. Saxena & I. Dimitriou & S. Kapodistria, 2020. "Analysis of the shortest relay queue policy in a cooperative random access network with collisions," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 39-75, February.
    10. Dieter Fiems & Balakrishna Prabhu & Koen Turck, 2013. "Analytic approximations of queues with lightly- and heavily-correlated autoregressive service times," Annals of Operations Research, Springer, vol. 202(1), pages 103-119, January.

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