Queueing Systems

, Volume 45, Issue 1, pp 47–57

Transient and Stationary Distributions for the GI/G/k Queue with Lebesgue-Dominated Inter-Arrival Time Distribution

  • Lothar Breuer

DOI: 10.1023/A:1025643801208

Cite this article as:
Breuer, L. Queueing Systems (2003) 45: 47. doi:10.1023/A:1025643801208


In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the embedded Markov chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the embedded Markov chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator–geometric stationary distribution. Thus it is shown that matrix–analytical methods can be extended to provide a modeling tool even for the general multi-server queue.

GI/G/kmulti-server queuediscrete time

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Lothar Breuer
    • 1
  1. 1.FB IV – InformatikUniversität TrierTrierGermany