Queueing Systems

, Volume 3, Issue 2, pp 179–198

Queues as Harris recurrent Markov chains

  • Karl Sigman
Contributed Papers

DOI: 10.1007/BF01189048

Cite this article as:
Sigman, K. Queueing Syst (1988) 3: 179. doi:10.1007/BF01189048

Abstract

We present a framework for representing a queue at arrival epochs as a Harris recurrent Markov chain (HRMC). The input to the queue is a marked point process governed by a HRMC and the queue dynamics are formulated by a general recursion. Such inputs include the cases of i.i.d, regenerative, Markov modulated, Markov renewal and the output from some queues as well. Since a HRMC is regenerative, the queue inherits the regenerative structure. As examples, we consider split & match, tandem, G/G/c and more general skip forward networks. In the case of i.i.d. input, we show the existence of regeneration points for a Jackson type open network having general service and interarrivai time distributions.

Keywords

Queuediscrete timeHarris recurrent Markov chainsregenerative

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1988

Authors and Affiliations

  • Karl Sigman
    • 1
  1. 1.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA