Analysis of the M/M/1 queue with inventory problem

Soufit, Massinissa,; Ouazine, Sofiane; Abbas, Karim

Séminaire Mathématique de Béjaia
Volume 16, Numéro 1, Pages 78-78
2018-12-31

Analysis Of The M/m/1 Queue With Inventory Problem

Authors : Soufit Massinissa, . Ouazine Sofiane . Abbas Karim .

Abstract

In this work, we provide an uncertainty analysis for queuing-inventory models, by extending the multivariate Taylor series expansion methodology to such stochastic models. Specifically, we derive a closed-form expression for the higher-order sensitivity of discrete-time Markov chain stationary distribution with respect to multiple parameters. We establish efficient bound on the remainder term corresponding to the multivariate Taylor series. Additionally, we estimate different quantities of interest of the output measures of the studied queuing-inventory model. Using the copulas theory, we also include the effect of the dependence structure of parameters. The efficacy of the proposed method is shown with several numerical examples and obtained numerical results are compared with those of Monte Carlo simulation.