Analysis of the Performance Parameters of Queueing Systems M/M/1 with Pre-Emptive Priority in Transient Regime

Abstract

In Markov chain theory, performance parameters are indicator of the proper management of a queue. In this field, an abundant literature exists, particularly in the steady state, which is not the case in the transient state. It is in this context that we can question whether it is possible to establish the equations of the performance measures in the transient regime with absolute priority given the complexity of the study of Markov chains in a transient regime. To achieve this, we used the analytical method based on the exploitation of the Laplace transform in the Kolmogorov equations, as well as the theory of convergent series in the equations resulting from the transition matrices. This analysis is supported by the descriptive technique. These tools allowed us to produce concrete results; which are the performance measures of priority and no priority customers in a transient regime M/M/1 queue. Which is a plus in the field of Markov chains. The purpose of this paper is to analyse the M/M/1 transient performance measures with absolute priority. Its originality lies in the fact that we have determined the expressions of the performance measures of non-priority customers in a transient regime. Indeed, very few publications are made in this area at this time. A numerical application was treated to illustrate the theory evoked above. This reflection could soon be carried out in a fuzzy environment.