Solving Ck/Cm/1/N queues by using characteristic roots in matrix analytic methods |
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Authors: | Hsing Luh Hsin-Yi Wang |
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Affiliation: | Department of Mathematical Sciences, National Chengchi University, Taipei 116, Taiwan |
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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. |
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Keywords: | Queues Phase-type probability distributions Matrix analytic methods Laplace transforms Vector product-forms |
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