Mean queue size in a queue with discrete autoregressive arrivals of order p

Jeongsim Kim, Bara Kim, Khosrow Sohraby

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We consider a discrete time single server queueing system where the arrival process is governed by a discrete autoregressive process of order p (DAR(p)), and the service time of a customer is one slot. For this queueing system, we give an expression for the mean queue size, which yields upper and lower bounds for the mean queue size. Further we propose two approximation methods for the mean queue size. One is based on the matrix analytic method and the other is based on simulation. We show, by illustrations, that the proposed approximations are very accurate and computationally efficient.

Original languageEnglish
Pages (from-to)69-83
Number of pages15
JournalAnnals of Operations Research
Issue number1
Publication statusPublished - 2008 Sept

Bibliographical note

Funding Information:
Acknowledgements The authors would like to thank Prof. Jesus Artalejo and anonymous referees for their valuable comments and suggestions to improve the paper. This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).


  • Discrete autoregressive process
  • Discrete time queueing system
  • Mean queue size

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research


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