Distribution of number served during a busy period of GI/M/1/N queues-lattice path approach

Abstract

Abstract This paper aims at transient analysis of finite queue GI/M/1/N by deriving the distribution of the number of customers served in a busy period. Lattice paths combinatorics is used, in which the process is split up at suitable renewable epochs and thus can be represented by a LP. The interarrival time distribution is approximated by two-phase Cox distribution, C2, that has Markovian property amenable to LP analysis. As distributions having rational Laplace–Stieltjes transforms and square coefficient of variation lying in [ 1 2 ,∞[ , forming a very wide class of distributions, can be approximated by C2, the use of C2 has yielded transient results applicable to almost any real life queueing system GI/M/1/N.