Distribution of Occupied Resources on A Discrete Resources Sharing in A Queueing System

Abstract

—In this paper, we study discrete resources sharing in a queueing system. We build analytical model of the distribution of occupied resources that can help for resources dimensioning. Both infinite and finite amount of discrete server resources are highlighted and validated with special cases of individual resource requirement following Poisson and Binomial distribution. It is found that there is a peak of usage near the average number of resources requested by customers, and other small peaks with low probability at multiples of this mean. The charging factor 𝝆 of the queue impacts mostly on the resources occupation distribution.