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

Jeongsim Kim, Bara Kim, Khosrow Sohraby

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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
Volume162
Issue number1
DOIs
Publication statusPublished - 2008 Sep 1

Fingerprint

Queue
Approximation
Queueing system
Lower bounds
Matrix analytic methods
Autoregressive process
Upper bound
Simulation
Discrete-time

Keywords

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

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Decision Sciences(all)

Cite this

Mean queue size in a queue with discrete autoregressive arrivals of order p. / Kim, Jeongsim; Kim, Bara; Sohraby, Khosrow.

In: Annals of Operations Research, Vol. 162, No. 1, 01.09.2008, p. 69-83.

Research output: Contribution to journalArticle

Kim, Jeongsim ; Kim, Bara ; Sohraby, Khosrow. / Mean queue size in a queue with discrete autoregressive arrivals of order p. In: Annals of Operations Research. 2008 ; Vol. 162, No. 1. pp. 69-83.
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