Strong Stability of Queues with Multiple Vacation of the Server |
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Authors: | Fazia Rahmoune Djamil Aissani |
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Institution: | 1. LAMOS, Laboratory of Modeling and Optimization of Systems , University of Beja?a , Targa Ouzemmour, Beja?a, Algeria foufourah@yahoo.fr;3. LAMOS, Laboratory of Modeling and Optimization of Systems , University of Beja?a , Targa Ouzemmour, Beja?a, Algeria |
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Abstract: | Abstract The main purpose of this article is to use the strong stability method to approximate the characteristics of the M/G/1//N queue with server vacation by those of the classical M/G/1//N queue, when the rate of the vacations is sufficiently small. This last queue is simpler and more exploitable in practice. For this, we proof the stability conditions and next obtain quantitative stability estimates with an exact computation of constants. From these theoretical results, we can develop an algorithm in order to check the conditions of approximation. These results of approximation have a great practical and economic interest in reliability systems and maintenance optimization policy, when we consider elements with constant failure rate. |
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Keywords: | Approximation Markov chains Queues with vacations Strong stability |
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