Abstract
Two approximative fixed-point iterative methods based on decomposition for closed queueing networks with Coxian service distributions and arbitrary buffer sizes are extended to include phase-type service distributions. The irreducible Markov chain associated with each subnetwork in the respective decompositions is represented hierarchically using Kronecker products. The two methods are implemented in a software tool capable of computing the steady-state probability vector of each subnetwork by a multilevel method at each fixed-point iteration and are compared with other methods for accuracy and efficiency. Numerical results indicate that there is a niche filled by the two approximative methods.
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The authors thank Jean-Michel Fourneau for pointing out Marie’s method and Brouwer’s fixed-point theorem. The first author gratefully acknowledges grant TÜBA-GEBİP from the Turkish Academy of Sciences.
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Dayar, T., Meriç, A. Kronecker representation and decompositional analysis of closed queueing networks with phase-type service distributions and arbitrary buffer sizes. Ann Oper Res 164, 193–210 (2008). https://doi.org/10.1007/s10479-008-0429-8
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DOI: https://doi.org/10.1007/s10479-008-0429-8