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

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

doi:10.1002/nav.21680

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

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

Rutgers Business School, Management & Information Systems

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 language	English (US)
Pages (from-to)	57-72
Number of pages	16
Journal	Naval Research Logistics
Volume	66
Issue number	1
DOIs	https://doi.org/10.1002/nav.21680
State	Published - Feb 1 2019

All Science Journal Classification (ASJC) codes

Modeling and Simulation
Ocean Engineering
Management Science and Operations Research

Keywords

Coxian interarrival times
QSF process
successively lumpable

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10.1002/nav.21680

Cite this

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title = "Level product form QSF processes and an analysis of queues with Coxian interarrival distribution",

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.",

keywords = "Coxian interarrival times, QSF process, successively lumpable",

author = "Dwi Ertiningsih and Katehakis, {Michael N.} and Smit, {Laurens C.} and Spieksma, {Flora M.}",

note = "Funding Information: We acknowledge support for this work from the National Science Foundation (NSF grant CMMI-14-50743) and the Directorate General of Human Resource for Science, Technology and Higher Education of the Ministry of National Education of Indonesia. Publisher Copyright: {\textcopyright} 2016 Wiley Periodicals, Inc.",

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AU - Ertiningsih, Dwi

AU - Katehakis, Michael N.

AU - Smit, Laurens C.

AU - Spieksma, Flora M.

N1 - Funding Information: We acknowledge support for this work from the National Science Foundation (NSF grant CMMI-14-50743) and the Directorate General of Human Resource for Science, Technology and Higher Education of the Ministry of National Education of Indonesia. Publisher Copyright: © 2016 Wiley Periodicals, Inc.

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N2 - 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.

AB - 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.

KW - Coxian interarrival times

KW - QSF process

KW - successively lumpable

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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