Regularly varying tails in a queue with discrete autoregressive arrivals of order p

Jeongsim Kim, Bara Kim

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We consider a discrete time single server queueing system where the service time of a customer is one slot, and the arrival process is governed by a discrete autoregressive process of order p (DAR(p)). For this queueing system, we investigate the tail behavior of the queue size and the waiting time distributions. Specifically, we show that if the stationary distribution of DAR(p) input has a tail of regular variation with index -β-1, then the stationary distributions of the queue size and the waiting time have tails of regular variation with index -β.

Original languageEnglish
Pages (from-to)93-102
Number of pages10
JournalQueueing Systems
Volume56
Issue number2
DOIs
Publication statusPublished - 2007 Jun

Keywords

  • Discrete autoregressive process
  • Discrete time queueing system
  • Regular variation

ASJC Scopus subject areas

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

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