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Bad luck when joining the shortest queue

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  • Blanc, J.P.C.

Abstract

A frequent observation in service systems with queues in parallel is that customers in other queues tend to be served faster than those in one's own queue. This paper quantifies the probability that one's service would have started earlier if one had joined another queue than the queue that was actually chosen, for exponential multiserver systems with queues in parallel in which customers join one of the shortest queues upon arrival and in which jockeying is not possible.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:195:y:2009:i:1:p:167-173
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    References listed on IDEAS

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    1. Blanc, J.P.C., 1993. "Performance Analysis and Optimization with the Power- Series Algorithm," Papers 9347, Tilburg - Center for Economic Research.
    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. Johri, Pravin K., 1989. "Optimality of the shortest line discipline with state-dependent service rates," European Journal of Operational Research, Elsevier, vol. 41(2), pages 157-161, July.
    4. 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.
    5. Yiqiang Zhao & W. K. Grassmann, 1990. "The shortest queue model with jockeying," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 773-787, October.
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    Citations

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    Cited by:

    1. de Palma, André & Fosgerau, Mogens, 2013. "Random queues and risk averse users," European Journal of Operational Research, Elsevier, vol. 230(2), pages 313-320.
    2. de Lange, Robert & Samoilovich, Ilya & van der Rhee, Bo, 2013. "Virtual queuing at airport security lanes," European Journal of Operational Research, Elsevier, vol. 225(1), pages 153-165.
    3. Ivo J. B. F. Adan & Onno J. Boxma & Stella Kapodistria & Vidyadhar G. Kulkarni, 2016. "The shorter queue polling model," Annals of Operations Research, Springer, vol. 241(1), pages 167-200, June.
    4. Jori Selen & Ivo Adan & Stella Kapodistria & Johan Leeuwaarden, 2016. "Steady-state analysis of shortest expected delay routing," Queueing Systems: Theory and Applications, Springer, vol. 84(3), pages 309-354, December.
    5. Tanaka, Masahiro & Yanagisawa, Daichi & Nishinari, Katsuhiro, 2018. "Exclusive queueing model including the choice of service windows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1481-1492.
    6. Hung, Ying-Chao & PakHai Lok, Horace & Michailidis, George, 2022. "Optimal routing for electric vehicle charging systems with stochastic demand: A heavy traffic approximation approach," European Journal of Operational Research, Elsevier, vol. 299(2), pages 526-541.

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    More about this item

    Keywords

    Queueing Join-the-shortest-queue Probability of bad luck Power-series algorithm Overtaking customers Dedicated customers;

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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