Lattice path approach to busy period density of queueing system \(C_2/C_2/1\) (Q948855)

Summary: The paper aims at busy period analysis of non-Markovian queuing system \(GI/G/1\) starting initially with \(i_0\) customers, through lattice path approach. Both interarrival and service time distributions are approximated by two-phase Cox distributions, \(C_2\), that have Markovian property, amenable to the application of lattice paths combinatorial analysis. Distributions having rational Laplace-Stieltjes transform and square coefficient of variation lying in \([1/2\infty \)) form a very wide class of distributions. As any distribution of this class can be approximated by \(C_2\), therefore, the use of \(C_2\) has led us to achieve results applicable to almost any real life queuing system \(GI/G/1\) 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 package Mathematica and represented graphically.