Busy period analysis of queue: Lattice path approach

In this paper, we find the busy period density of queues in explicit computational form, through lattice path (LP) approach. Both the arrival and service time distributions are approximated by 2-phase Cox distribution C₂, 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 (CV²) lying in 1/2,∞) can be approximated by a C₂(M. Agarwal, K. Sen, B. Borkakaty, Busy period density of queueing system C₃/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.