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Technical Note—Approximating Systems Fed by Poisson Processes with Rapidly Changing Arrival Rates

Author

Listed:
  • Zeyu Zheng

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720)

  • Harsha Honnappa

    (School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47906)

  • Peter W. Glynn

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

This paper introduces a new asymptotic regime for simplifying stochastic models having nonstationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the arrival process to a service system has an arrival intensity that is fluctuating rapidly. We show that such a service system is well approximated by the corresponding model in which the arrival process is Poisson with a constant arrival rate. In addition to the basic weak convergence theorem, we also establish a first order correction for the distribution of the cumulative number of arrivals over [ 0 , t ] , as well as the number-in-system process for an infinite-server queue fed by an arrival process having a rapidly changing arrival rate. This new asymptotic regime provides a second regime within which nonstationary stochastic models can be reasonably approximated by a process with stationary dynamics, thereby complementing the previously studied setting within which rates vary slowly in time.

Suggested Citation

  • Zeyu Zheng & Harsha Honnappa & Peter W. Glynn, 2021. "Technical Note—Approximating Systems Fed by Poisson Processes with Rapidly Changing Arrival Rates," Operations Research, INFORMS, vol. 69(5), pages 1566-1574, September.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:5:p:1566-1574
    DOI: 10.1287/opre.2020.2031
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