@inproceedings{c5bf33ffe4864f5195486c6a22a7cc0d,
title = "Fast solvers for queueing systems with negative customers",
abstract = "In this paper, we are interested in solving queueing systems having Poisson batch arrivals, exponential servers and negative customers. Preconditioned Conjugate Gradient (PCG) method is applied to solving the steady-state probability distribution of the queueing system. Preconditioners are constructed by exploiting near-Toeplitz structure of the generator matrix and the Gohberg-Semumcul formula. We proved that the preconditioned system has singular values clustered around one. Therefore Conjugate Gradient (CG) methods when applied to solving the preconditioned system, we expect fast convergence rate. Numerical examples are given to demonstrate our claim.",
keywords = "Gohberg-semencul formula, Negative customer, Preconditioned conjugate gradient method, Preconditioners, Queueing systems",
author = "Wen, {You Wei} and Ching, {Wai Ki} and NG, {Kwok Po}",
note = "Copyright: Copyright 2008 Elsevier B.V., All rights reserved.; VALUETOOLS: 1st International Conference on Performance Evaluation Methodologies and Tools ; Conference date: 11-10-2006 Through 13-10-2006",
year = "2006",
doi = "10.1145/1190095.1190111",
language = "English",
isbn = "1595935045",
series = "ACM International Conference Proceeding Series",
booktitle = "Proceedings of VALUETOOLS",
}