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Book Chapter10.1007/978-1-4612-5791-2_11

On Computing the Stationary Probability Vector of a Network of Two Coxian Servers

William J. Stewart-1982-01-01-Birkhäuser Boston eBooks
2

TL;DRAbstract

This paper presents an efficient direct method for the solution of a queueing network consisting of two Coxian servers. The structure of the transition rate matrix associated with this network is examined in some detail, and it is shown how advantage may be taken of this structure to derive the required stationary probability vector in a number of operations which is proportional to N, the number of customers in the network. The direct method which is employed, is based on a single step of inverse iteration. The method is shown to be stable.

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This paper presents an efficient direct method for the solution of a queueing network consisting of two Coxian servers. The structure of the transition rate matrix associated with this network is examined in some detail, and it is shown how advantage may be taken of this structure to derive the required stationary probability vector in a number of operations which is proportional to N, the number of customers in the network. The direct method which is employed, is based on a single step of inverse iteration. The method is shown to be stable.

Keywords

ServerComputer scienceQueueing theoryInverseLayered queueing networkApplied mathematicsMathematical optimizationComputer network

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