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Iterative Methods for Queuing Systems with Batch Arrivals and Negative Customers

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Abstract

In this paper, we are interested in solving the stationary probability distributions of Markovian queuing systems having batch arrivals and negative customers by using the Preconditioned Conjugate Gradient Squared (PCGS) method. The preconditioner is constructed by exploiting the near-Toeplitz structure of the generator matrix of the system. We proved that under some mild conditions the preconditioned linear systems have singular values clustered around one when the size of the queue tends to infinity. Numerical results indicated that the convergence rate of the proposed method is very fast.

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Authors and Affiliations

  1. Department of Mathematics, University of Hong Kong, Pokfulam Road, Hong Kong, China

    W. K. Ching

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  1. W. K. Ching
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Ching, W.K. Iterative Methods for Queuing Systems with Batch Arrivals and Negative Customers. BIT Numerical Mathematics 43, 285–296 (2003). https://doi.org/10.1023/A:1026031011953

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