The existence of fixed points for the ./GI/1 queue

• 成果类型: Article
• 署名作者: Mairesse, J; Prabhakar, B
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Stanford University; Stanford University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 2216-2236
• 关键词: NETWORKS; output

摘要

A celebrated theorem of Burke's asserts that the Poisson process is a fixed point for a stable exponential single server queue; that is, when the arrival process is Poisson, the equilibrium departure process is Poisson of the same rate. This paper considers the following question: Do fixed points exist for queues which dispense i.i.d. services of finite mean, but otherwise of arbitrary distribution (i.e., the so-called (.)/GI/1/infinity/FCFS queues)? We show that if the service time S is nonconstant and satisfies integralP{S greater than or equal to u}(1/2) du < infinity, then there is an unbounded set S subset of (E[S], infinity) such that for each alpha epsilon S there exists a unique ergodic fixed point with mean inter-arrival time equal to alpha. We conjecture that in fact S = (E[S], infinity).