Lattice Path Approach for Busy Period Density ofGIb/G/1 Queues UsingC2Coxian Distributions

Abstract

In this paper busy period analysis of non-Markovian queuing system GIb/G/1, starting initially with i0 batches of customers, is carried out via lattice path approach. Both interarrival and service time distributions are approximated by 2-phase Cox distributions, C2, that have Markovian property, amenable to the application of lattice paths combinatorial analysis. Arrivals occur in batches of size b. Distributions having rational Laplace-Stieltjes transform and square coefficient of variation lying in [1/2, ∞] form a very wide class of distributions. As any distribution of this class can be approximated by a C2, the use of C2, therefore, has led us to achieve results applicable to almost any real life queuing system GIb/G/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.