Title: Lattice path approach to busy period density of queueing system C₂/C₂/1

Authors: Manju Agarwal, Bidisha Borkakaty, Kanwar Sen

Addresses: Department of Operational Research, University of Delhi, Delhi 110007, India. ' Department of Operational Research, University of Delhi, Delhi 110007, India. ' Department of Statistics, University of Delhi, Delhi 110007, India

Abstract: 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.

Keywords: busy period analysis; GI/G/1; lattice path approach; two-phase Cox distribution; queuing systems.

DOI: 10.1504/IJOR.2008.019169

International Journal of Operational Research, 2008 Vol.3 No.5, pp.575 - 603

Published online: 01 Jul 2008 *

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