Busy period analysis of queue: Lattice path approach

In this paper, we find the busy period density of C 2 / C 2 b / 1 queues in explicit computational form, through lattice path (LP) approach. Both the arrival and service time distributions are approximated by 2-phase Cox distribution C 2 , which has a Markovian property enabling us to use LP combinatorics. Since any distribution with rational Laplace–Stieltjes transform (LST) and square coefficient of variation ( C V 2 ) lying in [ 1 / 2 , ∞ ) can be approximated by a C 2 ([M. Agarwal, K. Sen, B. Borkakaty, Busy period density of queueing system C 3 / M / 1 , Journal of Combinatorics, Information and Systems Sciences 31 (1–4) (2006) 127–161]), the results obtained would be applicable to a very wide class of distributions occurring in real life.