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Title: Solving Ck/Cm/1/N queues by using characteristic roots in matrix analytic methods
Authors: 陸行
Contributors: 應數系
Keywords: Queues;Phase-type probability distributions;Matrix analytic methods;Laplace transforms;Vector product-forms
Date: 2007.05
Issue Date: 2014-08-05 16:32:20 (UTC+8)
Abstract: In this paper, we study a Ck/Cm/1/N open queueing system with finite capacity. We investigate the property which shows that a product of the Laplace Stieltjes Transforms of interarrival and service times distributions satisfies an equation of a simple form. According to this equation, we present that the stationary probabilities on the unboundary states can be written as a linear combination of vector product-forms. Each component of these products is expressed in terms of roots of an associated characteristic polynomial. As a result, we carry out an algorithm for solving stationary probabilities in Ck/Cm/1/N systems, which is independent of N, hence greatly reducing the computational complexity.
Relation: Applied Mathematical Modelling,31(5),920-933
Data Type: article
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