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Level product form QSF processes and an analysis of queues with Coxian interarrival distribution

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  • Dwi Ertiningsih
  • Michael N. Katehakis
  • Laurens C. Smit
  • Flora M. Spieksma

Abstract

In this article, we study a class of Quasi‐Skipfree (QSF) processes where the transition rate submatrices in the skipfree direction have a column times row structure. Under homogeneity and irreducibility assumptions we show that the stationary distributions of these processes have a product form as a function of the level. For an application, we will discuss the Cox(k)/MY/1 ‐queue that can be modeled as a QSF process on a two‐dimensional state space. In addition, we study the properties of the stationary distribution and derive monotonicity of the mean number of the customers in the queue, their mean sojourn time and the variance as a function of k for fixed mean arrival rate. © 2016 Wiley Periodicals, Inc. Naval Research Logisticsxs 66:57–72, 2019

Suggested Citation

  • Dwi Ertiningsih & Michael N. Katehakis & Laurens C. Smit & Flora M. Spieksma, 2019. "Level product form QSF processes and an analysis of queues with Coxian interarrival distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 57-72, February.
    • Handle: RePEc:wly:navres:v:66:y:2019:i:1:p:57-72
    DOI: 10.1002/nav.21680
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    Cited by:

    1. Niek Baer & Ahmad Al Hanbali & Richard J. Boucherie & Jan-Kees van Ommeren, 2022. "A successive censoring algorithm for a system of connected LDQBD-processes," Annals of Operations Research, Springer, vol. 310(2), pages 389-410, March.

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