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Journal of Applied Mathematics
Volume 2012, Article ID 186761, 18 pages
Research Article

Efficient Method to Approximately Solve Retrial Systems with Impatience

1Departamento Automatica, Universidad de Alcalá, Alcalá de Henares, 28871 Madrid, Spain
2Departamento Comunicaciones, Universitat Politècnica de València, 46022 Valencia, Spain

Received 30 June 2011; Accepted 18 October 2011

Academic Editor: Nicola Guglielmi

Copyright © 2012 Jose Manuel Gimenez-Guzman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.