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

Dwi Ertiningsih, Michael Katehakis, Laurens C. Smit, Flora M. Spieksma

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 (Formula presented.) -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 (Formula presented.) for fixed mean arrival rate.

Original languageEnglish (US)
Pages (from-to)57-72
Number of pages16
JournalNaval Research Logistics
Volume66
Issue number1
DOIs
StatePublished - Feb 1 2019

Fingerprint

Product Form
Queue
Stationary Distribution
Sojourn Time
Irreducibility
Homogeneity
Monotonicity
State Space
Customers
Stationary distribution

All Science Journal Classification (ASJC) codes

  • Ocean Engineering
  • Modeling and Simulation
  • Management Science and Operations Research

Keywords

  • Coxian interarrival times
  • QSF process
  • successively lumpable

Cite this

Ertiningsih, Dwi ; Katehakis, Michael ; Smit, Laurens C. ; Spieksma, Flora M. / Level product form QSF processes and an analysis of queues with Coxian interarrival distribution. In: Naval Research Logistics. 2019 ; Vol. 66, No. 1. pp. 57-72.
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Level product form QSF processes and an analysis of queues with Coxian interarrival distribution. / Ertiningsih, Dwi; Katehakis, Michael; Smit, Laurens C.; Spieksma, Flora M.

In: Naval Research Logistics, Vol. 66, No. 1, 01.02.2019, p. 57-72.

Research output: Contribution to journalArticle

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