A matrix decomposition approach for solving state balance equations of a phase-type queueing model with multiple servers

Authors:
Yuan-Heng Yen;Hsing Paul Luh;Chia-Hung Wang
Affiliations:
National Chengchi University, Wenshan Dist., Taipei, Taiwan (R.O.C.);National Chengchi University, Wenshan Dist., Taipei, Taiwan (R.O.C.);National Chengchi University, Wenshan Dist., Taipei, Taiwan (R.O.C.)
Venue:
Proceedings of the 6th International Conference on Queueing Theory and Network Applications
Year:
2011

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Abstract

Stationary probabilities are fundamental in response to various measures of performance in queueing networks. Solving stationary probabilities in Quasi-Birth-and-Death (QBD) with phase-type distribution normally are dependent on the structure of the queueing network. In this paper, a new computing scheme is developed for attaining stationary probabilities in queueing networks with multiple servers. This scheme provides a general approach of considering the complexity of computing algorithm. The result becomes more significant when a large matrix is involved in computation. The background theorem of this approach is proved and provided with an illustrative example in this paper.