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Stationary-Process Approximations for the Nonstationary Erlang Loss Model

Author

Listed:
  • William A. Massey

    (Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey)

  • Ward Whitt

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

Abstract

In this paper we consider the M t / G / s /0 model, which has s servers in parallel, no extra waiting space, and i.i.d. service times that are independent of a nonhomogeneous Poisson arrival process. Arrivals finding all servers busy are blocked (lost). We consider approximations for the average blocking probabilities over subintervals (e.g., an hour when the expected service time is five minutes) obtained by replacing the nonstationary arrival process over that subinterval by a stationary arrival process. The stationary-Poisson approximation, using a Poisson ( M ) process with the average rate, tends to significantly underestimate the blocking probability. We obtain much better approximations by using a non-Poisson stationary ( G ) arrival process with higher stochastic variability to capture the effect of the time-varying deterministic arrival rate. In particular, we propose a specific approximation based on the heavy-traffic peakedness formula, which is easy to apply with either known arrival-rate functions or data from system measurements. We compare these approximations to exact numerical results for the M t / M / s /0 model with linear arrival rate.

Suggested Citation

  • William A. Massey & Ward Whitt, 1996. "Stationary-Process Approximations for the Nonstationary Erlang Loss Model," Operations Research, INFORMS, vol. 44(6), pages 976-983, December.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:6:p:976-983
    DOI: 10.1287/opre.44.6.976
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    Citations

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    Cited by:

    1. Itai Gurvich & Ohad Perry, 2012. "Overflow Networks: Approximations and Implications to Call Center Outsourcing," Operations Research, INFORMS, vol. 60(4), pages 996-1009, August.
    2. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    3. James Dong & Ward Whitt, 2015. "Using a birth‐and‐death process to estimate the steady‐state distribution of a periodic queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(8), pages 664-685, December.
    4. Guodong Pang & Ward Whitt, 2012. "The Impact of Dependent Service Times on Large-Scale Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 262-278, April.
    5. René Bekker & Paulien Koeleman, 2011. "Scheduling admissions and reducing variability in bed demand," Health Care Management Science, Springer, vol. 14(3), pages 237-249, September.
    6. Ward Whitt, 1999. "Improving Service by Informing Customers About Anticipated Delays," Management Science, INFORMS, vol. 45(2), pages 192-207, February.

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