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research
System-theoretical algorithmic solution to waiting times in semi-Markov queues
Authors
N. Akar
K. Sohraby
Publication date
1 January 2009
Publisher
'Elsevier BV'
Doi
Cite
Abstract
Cataloged from PDF version of article.Markov renewal processes with matrix-exponential semi-Markov kernels provide a generic tool for modeling auto-correlated interarrival and service times in queueing systems. In this paper, we study the steady-state actual waiting time distribution in an infinite capacity single-server semi-Markov queue with the auto-correlation in interarrival and service times modeled by Markov renewal processes with matrix-exponential kernels. Our approach is based on the equivalence between the waiting time distribution of this semi-Markov queue and the output of a linear feedback interconnection system. The unknown parameters of the latter system need to be determined through the solution of a SDC (Spectral-Divide-and-Conquer) problem for which we propose to use the ordered Schur decomposition. This approach leads us to a completely matrix-analytical algorithm to calculate the steady-state waiting time which has a matrix-exponential distribution. Besides its unifying structure, the proposed algorithm is easy to implement and is computationally efficient and stable. We validate the effectiveness and the generality of the proposed approach through numerical examples. © 2009 Elsevier B.V. All rights reserve
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Bilkent University Institutional Repository
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Last time updated on 12/11/2016
Bilkent University Institutional Repository
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:repository.bilkent.edu.tr:...
Last time updated on 12/11/2016