Lattice path approach for busy period density of GIa/Gb/1 queues using C2 Coxian distributions

In this paper busy period analysis of non-Markovian queueing system GI(a)/G(b)/1, starting initially with i(0) batches of customers, is carried out via lattice path approach. Both interarrival and service time distributions are approximated by 2-phase Cox distributions, C-2, that have Markovian property, amenable to the application of lattice paths combinatorial analysis. Arrivals occur in batches of size a and services occur in batches of size b, a and b are co-prime. Distributions having rational Laplace-Stieltjes transform and square coefficient of variation lying in [1/2, infinity) form a very wide class of distributions. As any distribution of this class can be approximated by a C-2, the use of C-2, therefore, has led us to achieve results applicable to almost any real life queueing system GI(a)/G(b)/1 occurring in computer systems, communication systems, manufacturing systems, etc. Numerical computations have been performed for different sets of values of the parameters involved using software Mathematica and presented graphically. (C) 2009 Published by Elsevier Inc.