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The Transient Behavior of the M / M / s Queue, with Implications for Steady-State Simulation

Author

Listed:
  • W. David Kelton

    (The University of Michigan, Ann Arbor, Michigan)

  • Averill M. Law

    (University of Arizona, Tucson, Arizona)

Abstract

Although the transient behavior of a queueing system is often of interest, available analytical results are usually quite restricted or are very complicated. We consider the M / M / s queue with an arbitrary number of customers present at time zero. We obtain probabilities in a relatively simple closed form that can be used to evaluate exactly several measures of system performance, including the expected delay in queue of each arriving customer. A numerical examination is carried out to see how the choice of initial condition affects the nature of convergence of the expected delays to their steady-state values. We also discuss the implications of these results for the initialization of steady-state simulations.

Suggested Citation

  • W. David Kelton & Averill M. Law, 1985. "The Transient Behavior of the M / M / s Queue, with Implications for Steady-State Simulation," Operations Research, INFORMS, vol. 33(2), pages 378-396, April.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:2:p:378-396
    DOI: 10.1287/opre.33.2.378
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    Citations

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    Cited by:

    1. B. Legros, 2022. "The Transient Blended Queue," Post-Print hal-04452674, HAL.
    2. William H. Kaczynski & Lawrence M. Leemis & John H. Drew, 2012. "Transient Queueing Analysis," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 10-28, February.
    3. Christos Zacharias & Michael Pinedo, 2017. "Managing Customer Arrivals in Service Systems with Multiple Identical Servers," Manufacturing & Service Operations Management, INFORMS, vol. 19(4), pages 639-656, October.
    4. Chaithanya Bandi & Nikolaos Trichakis & Phebe Vayanos, 2019. "Robust Multiclass Queuing Theory for Wait Time Estimation in Resource Allocation Systems," Management Science, INFORMS, vol. 65(1), pages 152-187, January.
    5. Chaithanya Bandi & Dimitris Bertsimas & Nataly Youssef, 2018. "Robust transient analysis of multi-server queueing systems and feed-forward networks," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 351-413, August.
    6. Rowan Wang & Oualid Jouini & Saif Benjaafar, 2014. "Service Systems with Finite and Heterogeneous Customer Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 365-380, July.
    7. Sandikci, Burhaneddin & Sabuncuoglu, Ihsan, 2006. "Analysis of the behavior of the transient period in non-terminating simulations," European Journal of Operational Research, Elsevier, vol. 173(1), pages 252-267, August.

    More about this item

    Keywords

    700 simulation; 704 transient results;

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