Waiting time asymptotics in the single server queue with service in random order

O. J. Boxma, S. G. Foss, J. M. Lasgouttes, R. Núñez Queija

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals and regularly varying service time distribution with index -v, it is shown that the waiting time distribution is also regularly varying, with index 1 - v, and the pre-factor is determined explicitly. Another contribution of the paper is the heavy-traffic analysis of the waiting time distribution in the M/G/1 case. We consider not only the case of finite service time variance, but also the case of regularly varying service time distribution with infinite variance.

Original languageEnglish
Pages (from-to)35-73
Number of pages39
JournalQueueing Systems
Volume46
Issue number1-2
Publication statusPublished - Jan 2004

Keywords

  • Heavy-tailed distribution
  • Heavy-traffic limit theorem
  • Service in random order
  • Single server queue
  • Waiting time asymptotics

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  • Cite this

    Boxma, O. J., Foss, S. G., Lasgouttes, J. M., & Núñez Queija, R. (2004). Waiting time asymptotics in the single server queue with service in random order. Queueing Systems, 46(1-2), 35-73.