Lattice path approach to transient analysis of M/G/1/N non-Markovian queues using Cox distributions

Abstract

In this paper, on approximating the general service time distribution by Coxian two-phase distribution, C 2 , explicit busy period density function for non-Markovian finite queues M/G/1/ N has been obtained by using lattice paths combinatorics (LPC). The results obtained are specifically important as it seems that no explicit transient solutions are available for finite queues. Two-phase Cox distribution, C 2 , has Markovian property and is thus amenable to lattice path (LP) analysis. The transient results obtained are applicable to almost any real life finite queuing system M/G/1/ N .