Perfect sampling for infinite server and loss systems

Jose Blanchet, Jing Dong

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.

Original languageEnglish (US)
Pages (from-to)761-786
Number of pages26
JournalAdvances in Applied Probability
Volume47
Issue number3
DOIs
StatePublished - Sep 2015

Keywords

  • Dominated coupling from the past
  • Infinite server queue
  • Loss queue
  • Many-server asymptotics
  • Perfect sampling
  • Renewal point process

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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