Heavy-traffic fluid limits for periodic infinite-server queues

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• 作者：Ward Whitt
• 关键词：Stochastic grey ; box queueing models ; Periodic queues ; Periodic arrival rates ; Periodic steady state ; Birth ; and ; death processes ; Fitting birth ; and ; death processes to data ; Many ; server heavy ; traffic limits
• 刊名：Queueing Systems
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：84
• 期：1-2
• 页码：111-143
• 全文大小：825 KB
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Operation Research and Decision Theory
  Computer Communication Networks
  Probability Theory and Stochastic Processes
  Production and Logistics
  Systems Theory and Control
  
• 出版者：Springer Netherlands
• ISSN：1572-9443
• 卷排序：84

文摘

To better understand what stochastic model might be appropriate in applications with system data, we study the consequences of fitting a stationary birth-and-death (BD) process to the sample path of a periodic \(M_t/GI/\infty \) model. The fitted BD process will necessarily have the correct steady-state distribution (appropriately defined), but will not have the correct transient behavior. Nevertheless, the fitted birth-rate and death-rate functions have structure determined by the \(M_t/GI/\infty \) model that should be seen with data if the \(M_t/GI/\infty \) model is appropriate. In this paper, we establish heavy-traffic fluid limits that yield explicit approximation formulas for the fitted birth-rate and death-rate functions that can help evaluate whether a periodic \(M_t/GI/\infty \) model is appropriate. We also establish many-server heavy-traffic fluid limits for the steady-state distribution in the periodic \(M_t/GI/\infty \) model. For the special case of sinusoidal arrival rates, the limiting steady-state distribution has an arcsine law.