A queueing system with discrete autoregressive arrivals

Bara Kim, Yong Chang, Yeong Cheol Kim, Bong Dae Choi

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We consider a discrete time single server queue with discrete autoregressive process of order 1 (DAR(1)) input. By extracting a Markov process from the queue size process and applying the BASTA property, we derive simple recursive formulae for the stationary distributions of the queue size and the waiting time. These formulae are simple, numerically stable and transform-free. A stochastic decomposition property is given for the stationary waiting time, and relations between the distributions of the stationary queue size and the stationary waiting time are discussed. Numerical examples are given for stationary distributions of the queue size and the waiting time for various DAR(1) inputs.

Original languageEnglish
Pages (from-to)148-161
Number of pages14
JournalPerformance Evaluation
Issue number2
Publication statusPublished - 2007 Feb


  • DAR(1)
  • Discrete time queue
  • Queue size
  • Recursive formula
  • Stochastic decomposition
  • Waiting time

ASJC Scopus subject areas

  • Software
  • Modelling and Simulation
  • Hardware and Architecture
  • Computer Networks and Communications


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