Abstract
Abstract This paper aims at deriving explicit transient queue length distribution for GI/M/1 system and busy period analysis of bulk queue GIb/M/1 through lattice paths (LPs) combinatorics. The general interarrival time distribution is approximated by two-phase Cox distribution, C2, that has Markovian property, enabling us to represent the processes by two-dimensional LPs. As distributions C2 cover a wide class of distributions that have rational Laplace–Stieltjes transforms (LSTs) with square coefficient of variation lying in [ 1 2 ,∞) , the results obtained are applicable to a large class of real life situations. Some numerical results for the C2b/M/1 model are also given.
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