The paper aims at busy period analysis of non‐Markovian queuing system GI/G/1 starting initially with i0 customers, through lattice path approach. Both interarrival and service time distributions are approximated by two‐phase Cox distributions, C2, 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∞) form a very wide class of distributions. As any distribution of this class can be approximated by C2, therefore, the use of C2 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.
