Queues with boundary assistance: The effects of truncation

G Latouche; GT Nguyen; PG Taylor

Journal article

Queues with boundary assistance: The effects of truncation

G Latouche, GT Nguyen, PG Taylor

Queueing Systems | SPRINGER | Published : 2011

DOI: 10.1007/s11134-011-9255-9

Abstract

We study a system of two queues with boundary assistance, represented as a continuous-time Quasi-Birth-and-Death process (QBD). Under our formulation, this QBD has a 'doubly infinite' number of phases. We determine the convergence norm of Neuts' R-matrix and, consequently, the interval in which the decay rate of the infinite system can lie. We next consider four sequences of finite-phase approximations to the original system in which the Nth approximation has 2N+1 phases; one is derived by truncating the infinite system without augmentation, the others are obtained by using different augmentation schemes that ensure that the generator of the QBD remains conservative. The sequences of matrice..

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University of Melbourne Researchers

Peter Taylor Author

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Advanced matrix-analytic methods with applications

Over the last twenty-five years, matrix-analytic methods have proved to be very successful in formulating and analysing certain classes of s..

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Awarded by Appalachian Regional Commission

Funding Acknowledgements

This work has been subsidized by the ARC grant AUWB-08/13-ULB 5 financed by the Ministere de la Communaute francaise de Belgique. The authors acknowledge the support of Australian Research Council Grant DP110101663. The second author also gratefully acknowledges the support from Fonds de la Recherche Scientifique.