Transient Busy Period Analysis of Initially Non-Empty M/G/l Queues—Lattice Path Approach

This paper aims at transient busy period analysis of M/G/l queueing systems starting initially with i customers through lattice path approach. The service time distribution is approximated by a 2-phase Cox distribution, C₂. Distributions having rational Laplace-Stieltjes transforms and square coefficient of variation lying in $$\left. {\frac{1}{2},\infty } \right)$$ form a very wide class of distributions. As any distribution of this class can be approximated by a C₂, that has Markovian property, amenable to the application of lattice paths combinatorial analysis, the use of C₂ therefore has led us to achieve transient results applicable to almost any real life queueing system M/G/l.