Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds

Guodong Pang, Yuhang Zhou

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Abstract

We prove two-parameter process limits for infinite-server queues with weakly dependent service times satisfying the ρ-mixing condition. The two-parameter processes keep track of the elapsed or residual service times of customers in the system. We use the new methodology developed in Pang and Zhou (Stoch Process Appl 127(5):1375–1416, 2017) to prove weak convergence of two-parameter stochastic processes. Specifically, we employ the maximal inequalities for two-parameter queueing processes resulting from the method of chaining. This new methodology requires a weaker mixing condition on the service times than the ϕ-mixing condition in Pang and Whitt (Queueing Syst 73(2):119–146, 2013), as well as fewer regularity conditions on the service time distribution function.

Original languageEnglish (US)
JournalQueueing Systems
Volume88
Issue number1-2
DOIs
Publication statusPublished - Feb 1 2018

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics

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