On the Solution to QBD Processes with Finite State Space |
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Authors: | Essia H Elhafsi Mart Molle |
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Institution: | 1. Department of Computer Science and Engineering , University of California , Riverside, California, USA essia@cs.ucr.edu;3. Department of Computer Science and Engineering , University of California , Riverside, California, USA |
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Abstract: | Abstract In this article, we present a solution to a class of Quasi-Birth-and-Death processes with finite state space and show that the stationary probability vector has a matrix geometric representation. We show that such models have a level-dependent rate matrix. The corresponding rate matrix is given explicitly in terms of the model parameters. The resulting closed-form expression is proposed as a basis for efficient calculation of the stationary probabilities. The method proposed in this article can be applied to several queueing systems. |
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Keywords: | Closed-form solution Computation complexity Markov chain Matrix geometric |
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