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Exponential Approximations for Tail Probabilities in Queues II: Sojourn Time and Workload

Author

Listed:
  • Joseph Abate

    (Ridgewood, New Jersey)

  • Gagan L. Choudhury

    (AT&T Laboratories, Holmdel, New Jersey)

  • Ward Whitt

    (AT&T Laboratories, Murray Hill, New Jersey)

Abstract

We continue to focus on simple exponential approximations for steady-state tail probabilities in queues based on asymptotics. For the G / GI /1 model with i.i.d. service times that are independent of an arbitrary stationary arrival process, we relate the asymptotics for the steady-state waiting time, sojourn time, and workload. We show that the three asymptotic decay rates coincide and that the three asymptotic constants are simply related. We evaluate the exponential approximations based on the exact asymptotic parameters and their approximations by making comparisons with exact numerical results for BMAP / G /1 queues, which have batch Markovian arrival processes. Numerical examples show that the exponential approximations for the tail probabilities are remarkably accurate at the 90th percentile and beyond. Thus, these exponential approximations appear very promising for applications.

Suggested Citation

  • Joseph Abate & Gagan L. Choudhury & Ward Whitt, 1996. "Exponential Approximations for Tail Probabilities in Queues II: Sojourn Time and Workload," Operations Research, INFORMS, vol. 44(5), pages 758-763, October.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:5:p:758-763
    DOI: 10.1287/opre.44.5.758
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    Cited by:

    1. Aouam, Tarik & Kumar, Kunal, 2019. "On the effect of overtime and subcontracting on supply chain safety stocks," Omega, Elsevier, vol. 89(C), pages 1-20.
    2. Søren Asmussen & Colm O'cinneide, 2002. "On the Tail of the Waiting Time in a Markov-Modulated M/G/1 Queue," Operations Research, INFORMS, vol. 50(3), pages 559-565, June.
    3. Gad Allon & Awi Federgruen, 2008. "Service Competition with General Queueing Facilities," Operations Research, INFORMS, vol. 56(4), pages 827-849, August.
    4. Jalili Marand, Ata & Tang, Ou & Li, Hongyan, 2019. "Quandary of service logistics: Fast or reliable?," European Journal of Operational Research, Elsevier, vol. 275(3), pages 983-996.
    5. Asmussen, Søren & Klüppelberg, Claudia & Sigman, Karl, 1999. "Sampling at subexponential times, with queueing applications," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 265-286, February.
    6. Jalili Marand, Ata & Li, Hongyan & Thorstenson, Anders, 2019. "Joint inventory control and pricing in a service-inventory system," International Journal of Production Economics, Elsevier, vol. 209(C), pages 78-91.
    7. So, Kut C. & Song, Jing-Sheng, 1998. "Price, delivery time guarantees and capacity selection," European Journal of Operational Research, Elsevier, vol. 111(1), pages 28-49, November.
    8. Jianpei Wen & Hanyu Jiang & Jie Song, 2019. "A Stochastic Queueing Model for Capacity Allocation in the Hierarchical Healthcare Delivery System," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-24, February.
    9. Bart Steyaert & Sabine Wittevrongel & Herwig Bruneel, 2017. "Characterisation of the output process of a discrete-time GI / D / 1 queue, and its application to network performance," Annals of Operations Research, Springer, vol. 252(1), pages 175-190, May.

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