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Using Robust Queueing to Expose the Impact of Dependence in Single-Server Queues

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  • Ward Whitt

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Wei You

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

Queueing applications are often complicated by dependence among interarrival times and service times. Such dependence is common in networks of queues, where arrivals are departures from other queues or superpositions of such complicated processes, especially when there are multiple customer classes with class-dependent service-time distributions. We show that the robust queueing approach for single-server queues proposed in the literature can be extended to yield improved steady-state performance approximations in the standard stochastic setting that includes dependence among interarrival times and service times. We propose a new functional robust queueing formulation for the steady-state workload that is exact for the steady-state mean in the M / GI /1 model and is asymptotically correct in both heavy traffic and light traffic. Simulation experiments show that it is effective more generally. The online appendix is available at https://doi.org/10.1287/opre.2017.1649 .

Suggested Citation

  • Ward Whitt & Wei You, 2018. "Using Robust Queueing to Expose the Impact of Dependence in Single-Server Queues," Operations Research, INFORMS, vol. 66(1), pages 184-199, January.
    • Handle: RePEc:inm:oropre:v:66:y:2018:i:1:p:184-199
    DOI: 10.1287/opre.2017.1649
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    References listed on IDEAS

    as
    1. Ward Whitt, 1995. "Variability Functions for Parametric-Decomposition Approximations of Queueing Networks," Management Science, INFORMS, vol. 41(10), pages 1704-1715, October.
    2. Chaithanya Bandi & Dimitris Bertsimas & Nataly Youssef, 2015. "Robust Queueing Theory," Operations Research, INFORMS, vol. 63(3), pages 676-700, June.
    3. Song-Hee Kim & Ward Whitt, 2014. "Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 464-480, July.
    4. Ward Whitt, 1984. "Approximations for departure processes and queues in series," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(4), pages 499-521, December.
    5. Whitt, Ward, 1985. "Queues with superposition arrival processes in heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 81-91, December.
    6. Gabriel R. Bitran & Devanath Tirupati, 1988. "Multiproduct Queueing Networks with Deterministic Routing: Decomposition Approach and the Notion of Interference," Management Science, INFORMS, vol. 34(1), pages 75-100, January.
    7. Ward Whitt, 1989. "Planning Queueing Simulations," Management Science, INFORMS, vol. 35(11), pages 1341-1366, November.
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    Cited by:

    1. Chenguang (Allen) Wu & Achal Bassamboo & Ohad Perry, 2019. "Service System with Dependent Service and Patience Times," Management Science, INFORMS, vol. 65(3), pages 1151-1172, March.
    2. Civelek, Ismail & Biller, Bahar & Scheller-Wolf, Alan, 2021. "Impact of dependence on single-server queueing systems," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1031-1045.
    3. 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.
    4. Itai Gurvich & John J. Hasenbein, 2022. "Policy robustness in queueing networks," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 425-427, April.
    5. Ward Whitt & Wei You, 2022. "New decomposition approximations for queueing networks," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 365-367, April.

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