NDLI: Queuing Systems Having Phase-Dependent Arrival and Service Rates

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Queuing Systems Having Phase-Dependent Arrival and Service Rates

Content Provider	Scilit
Author	Daigle, John N. Lucantoni, David M.
Copyright Year	2021
Description	The behavior of many systems of practical interest in communications and other areas is well modeled by a single-server exponential queuing system in which the arrival and service rates are dependent upon the state of a Markov chain, the dynamics of which are independent of the queue length. Formal solutions to such models based on Neuts's matrix geometric approach have appeared frequently in the literature. A major problem in using the matrix geometric approach is the computation of the rate matrix, which requires the solution of a matrix polynomial. In particular, computational times appear to be unpredictable and excessive for many problems of practical interest, especially under heavy traffic loads. In this paper, we present an efficient method of determining the rate matrix that performs well at all traffic loads. We then show how the rate matrix may be applied to determine not only the joint and marginal queue distributions, but also many other quantities of practical interest, such as the virtual and stochastic equilibrium waiting time 162distributions. We present numerical examples that illustrate the application of our techniques. Book Name: Numerical Solution of Markov Chains
Related Links	https://api.taylorfrancis.com/content/chapters/edit/download?identifierName=doi&identifierValue=10.1201/9781003210160-10&type=chapterpdf
Ending Page	202
Page Count	42
Starting Page	161
DOI	10.1201/9781003210160-10
Language	English
Publisher	Informa UK Limited
Publisher Date	2021-06-16
Access Restriction	Open
Subject Keyword	Book Name: Numerical Solution of Markov Chains Operations Research and Management Science Transportation Models Behavior Arrival Geometric Queuing Matrix Practical Interest
Content Type	Text
Resource Type	Chapter

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