Iterative methods for queueing models with batch arrivals
Refereed conference paper presented and published in conference proceedings

香港中文大學研究人員

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摘要We consider finding the stationary probability distribution vectors of Markovian queueing models having batch arrivals by using the preconditioned conjugate gradient (PCG) method. The preconditioners are constructed by exploiting the near-Toeplitz structure of the generator matrix of the model and are products of circulant matrices and band-Toeplitz matrices. We prove that if the number of servers s is fixed independent of the queue size n, then for sufficiently large n, the preconditioners are invertible and the preconditioned systems have singular values clustered around 1. Hence if the systems are solved by the preconditioned conjugate gradient method, we expect superlinear convergence. Our numerical results show that the PCG method with our preconditioner converges in finite number of steps independent of n and s whereas the numbers required by the Jacobi method or the PCG method without any preconditioner increase like O(n).
著者Chan RH, Ching WK
會議名稱2nd International Workshop on the Numerical Solution of Markov Chains
會議開始日18.01.1995
會議地點RALEIGH
會議國家/地區美國
詳細描述ed. by W. Stewart.
出版年份1995
月份1
日期1
出版社KLUWER ACADEMIC PUBL
頁次81 - 93
國際標準書號0-7923-9550-6
語言英式英語
Web of Science 學科類別Computer Science; Computer Science, Software Engineering; Mathematics

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