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Time-Varying Robust Queueing

Author

Listed:
  • Ward Whitt

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

  • Wei You

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

Abstract

We develop a time-varying robust-queueing (TVRQ) algorithm for the continuous-time workload in a single-server queue with a time-varying arrival-rate function. We apply this TVRQ to develop approximations for the periodic steady-state expected workload in models with a periodic arrival-rate function. We apply simulation and asymptotic methods to examine the performance of periodic TVRQ (PRQ). We find that PRQ predicts the mean of the periodic distribution and even the full distribution (specified by the quantiles) remarkably well. We show that the PRQ converges to a proper limit in appropriate long-cycle and heavy-traffic regimes and coincides with long-cycle fluid limits and heavy-traffic diffusion limits for long cycles.

Suggested Citation

  • Ward Whitt & Wei You, 2019. "Time-Varying Robust Queueing," Operations Research, INFORMS, vol. 67(6), pages 1766-1782, November.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:6:p:1766-1782
    DOI: 10.1287/opre.2019.1846
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    References listed on IDEAS

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    Cited by:

    1. Kerry Fendick & Ward Whitt, 2022. "Heavy traffic limits for queues with non-stationary path-dependent arrival processes," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 113-135, June.
    2. Yacov Satin & Rostislav Razumchik & Ilya Usov & Alexander Zeifman, 2023. "Numerical Computation of Distributions in Finite-State Inhomogeneous Continuous Time Markov Chains, Based on Ergodicity Bounds and Piecewise Constant Approximation," Mathematics, MDPI, vol. 11(20), pages 1-12, October.
    3. Alexander Zeifman & Yacov Satin & Ivan Kovalev & Rostislav Razumchik & Victor Korolev, 2020. "Facilitating Numerical Solutions of Inhomogeneous Continuous Time Markov Chains Using Ergodicity Bounds Obtained with Logarithmic Norm Method," Mathematics, MDPI, vol. 9(1), pages 1-20, December.
    4. Hu, Shichun & Dessouky, Maged M. & Uhan, Nelson A. & Vayanos, Phebe, 2021. "Cost-sharing mechanism design for ride-sharing," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 410-434.
    5. Zeifman, A.I. & Razumchik, R.V. & Satin, Y.A. & Kovalev, I.A., 2021. "Ergodicity bounds for the Markovian queue with time-varying transition intensities, batch arrivals and one queue skipping policy," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    6. 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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