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

• 成果类型: Article
• 署名作者: Zheng, Zeyu; Honnappa, Harsha; Glynn, Peter W.
• 署名单位: University of California System; University of California Berkeley; Purdue University System; Purdue University; Stanford University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2020.2031
• 发表日期: 2021
• 页码: 1566-1574
• 关键词: infinite-server queues; queuing-networks; STABILITY; expansions

摘要

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.