Séminaire Mathématique de Béjaia
Volume 13, Numéro 1, Pages 21-27
2014-12-31
An Optimal Approximation Of The Characteristics Of The Gi/m/1 Queue With Two-stage Service Policy
Authors : Cherfaoui Mouloud . Bareche Aicha . Aïssani Djamil . Adjabi Smail .
Abstract
In this work, we consider an GI/M/1 system with two-stage service policy, having a rate service (µ1; µ2), with using the strong stability method we establish the approximation conditions for the stationary characteristics of this system by those of the standard GI/M/1 system. Under assumption that the approximation conditions are satis ed, we give the estimate of the deviation (stability inequalities) between the stationary distribution of the GI/M/1 system with two-stage service policy and those of the standard GI/M/1 system for three considered cases : the standard system has a service rate µ1, the standard system has a service rate µ2 and the standard system has a service rate µ* minimizing the deviation. To calculate these deviations, the situation is modeled by a mathematical optimization problem that belongs to the minimization of a constrained nonlinear multi-variable function. Finally, numerical studies are performed to support the theoretical obtained results.
Keywords
G-queue ; Perturbation ; Strong stability ; Constrained nonlinear optimization.
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