Efficient Method to Approximately Solve Retrial Systems with Impatience
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 Kolmogoro...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/186761 |
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| author | Jose Manuel Gimenez-Guzman M. Jose Domenech-Benlloch Vicent Pla Jorge Martinez-Bauset Vicente Casares-Giner |
| author_facet | Jose Manuel Gimenez-Guzman M. Jose Domenech-Benlloch Vicent Pla Jorge Martinez-Bauset Vicente Casares-Giner |
| author_sort | Jose Manuel Gimenez-Guzman |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-48f10dfd6a6542c6ad10b4256b85f01b |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-48f10dfd6a6542c6ad10b4256b85f01b2025-02-03T07:25:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/186761186761Efficient Method to Approximately Solve Retrial Systems with ImpatienceJose Manuel Gimenez-Guzman0M. Jose Domenech-Benlloch1Vicent Pla2Jorge Martinez-Bauset3Vicente Casares-Giner4Departamento Automatica, Universidad de Alcalá, Alcalá de Henares, 28871 Madrid, SpainDepartamento Comunicaciones, Universitat Politècnica de València, 46022 Valencia, SpainDepartamento Comunicaciones, Universitat Politècnica de València, 46022 Valencia, SpainDepartamento Comunicaciones, Universitat Politècnica de València, 46022 Valencia, SpainDepartamento Comunicaciones, Universitat Politècnica de València, 46022 Valencia, SpainWe 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.http://dx.doi.org/10.1155/2012/186761 |
| spellingShingle | Jose Manuel Gimenez-Guzman M. Jose Domenech-Benlloch Vicent Pla Jorge Martinez-Bauset Vicente Casares-Giner Efficient Method to Approximately Solve Retrial Systems with Impatience Journal of Applied Mathematics |
| title | Efficient Method to Approximately Solve Retrial Systems with Impatience |
| title_full | Efficient Method to Approximately Solve Retrial Systems with Impatience |
| title_fullStr | Efficient Method to Approximately Solve Retrial Systems with Impatience |
| title_full_unstemmed | Efficient Method to Approximately Solve Retrial Systems with Impatience |
| title_short | Efficient Method to Approximately Solve Retrial Systems with Impatience |
| title_sort | efficient method to approximately solve retrial systems with impatience |
| url | http://dx.doi.org/10.1155/2012/186761 |
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