Journal of Applied Mathematics

Efficient Method to Approximately Solve Retrial Systems with Impatience

Jose Manuel Gimenez-Guzman, M. Jose Domenech-Benlloch, Vicent Pla, Jorge Martinez-Bauset, and Vicente Casares-Giner

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We present a novel technique to solve multiserver retrial systems with impatience. Unfortunately these systems do not present an exact analytic solution, so it is mandatory to resort to approximate techniques. This novel technique does not rely on the numerical solution of the steady-state Kolmogorov equations of the Continuous Time Markov Chain as it is common for this kind of systems but it considers the system in its Markov Decision Process setting. This technique, known as value extrapolation, truncates the infinite state space using a polynomial extrapolation method to approach the states outside the truncated state space. A numerical evaluation is carried out to evaluate this technique and to compare its performance with previous techniques. The obtained results show that value extrapolation greatly outperforms the previous approaches appeared in the literature not only in terms of accuracy but also in terms of computational cost.

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J. Appl. Math., Volume 2012 (2012), Article ID 186761, 18 pages.

First available in Project Euclid: 17 October 2012

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Gimenez-Guzman, Jose Manuel; Domenech-Benlloch, M. Jose; Pla, Vicent; Martinez-Bauset, Jorge; Casares-Giner, Vicente. Efficient Method to Approximately Solve Retrial Systems with Impatience. J. Appl. Math. 2012 (2012), Article ID 186761, 18 pages. doi:10.1155/2012/186761.

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