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Lattice path approach for busy period density of GIa/Gb/1 queues using C2 Coxian distributions

Bidisha Borkakaty
Manju Agarwal
Kanwar Sen
Journal / Anthology

Applied Mathematical Modeling
Year: 2010
Volume: 34
Issue: 6
Page range: 1597-1614

In this paper busy period analysis of non-Markovian queueing system GIa=Gb=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 a and services occur in batches of size b; a and b are co-prime. Distributions having rational Laplace–Stieltjes transform and square coefficient of variation lying in ½1=2;1Ž 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 queueing system GIa=Gb=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.