a Department of Statistics, Faculty of Mathematical Sciences, University of Delhi, Delhi-110007, India
b Department of Operational Research, Faculty of Mathematical Sciences, University of Delhi, Delhi-110007, India
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
, 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.