Abstract

In this paper, two new formulations of the steady-state probability distribution of the number of customers in an M/E-r/1 queue system are presented. On one hand, a new recurrent method which is numerically stable and computationally more efficient than the existing ones, in terms of memory and time, is presented. On the other hand, a new analytic formula, simpler than the current ones, which additionally has associated a probabilistic interpretation of its terms, that gives a new insight about this queue and its behavior, is also presented. (C) 2014 Elsevier B.V. All rights reserved.