Busy period analysis of C2/C2b/1 queue: Lattice path approach

In this paper, we find the busy period density of C2/C2b/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 C2C2, 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)(CV2) lying in [1/2,∞)[1/2,∞) can be approximated by a C2C2([M. Agarwal, K. Sen, B. Borkakaty, Busy period density of queueing system C3/M/1C3/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.