Perturbation Bounds For Gi/m/s Queue: The Strong Stability Method

Résumé: This paper investigates when the M/M/s model can be used to predict an estimate for the proximity of the performance measures of queues with arrival processes that are slightly different from the Poisson process assumed in the model. The arrival processes considered here are perturbed Poisson processes. The perturbations are deviations from the exponential distribution of the inter-arrival times or from the assumption of independence between successive inter-arrival times. In this work, we apply the strong stability method to obtain an estimate for the proximity of the performance measures in the GI/M/s queueing system to the same performance measures in the M/M/s system under the assumption that the distributions of the arrival time are close and the service flows coincide. In addition to the proof of the stability fact for the perturbed M/M/s queueing system, we obtain the inequalities of the stability. These results give with precision the error, on the queue size stationary distribution, due to the approximation.

Publié dans la revue: Séminaire Mathématique de Béjaia