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Journal of Statistical Theory and Practice

, Volume 1, Issue 2, pp 167–198 | Cite as

Lattice Path Approach for Busy Period Density of GIb/G/1 Queues Using C2 Coxian Distributions

  • Manju Agarwal
  • Kanwar Sen
  • Bidisha Borkakaty
Article

Abstract

In this paper busy period analysis of non-Markovian queuing system GIb/G/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 b. 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 a C2, the use of C2, therefore, has led us to achieve results applicable to almost any real life queuing system GIb/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 Mathematica and presented graphically.

AMS Subject Classification

60K25 

Keywords

Lattice Path Approach Busy Period Analysis Batch Arrivals 2-phase Cox Distribution C2, GIb/G/1 

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Copyright information

© Grace Scientific Publishing 2007

Authors and Affiliations

  1. 1.Department of Operational ResearchUniversity of DelhiDelhiIndia
  2. 2.Department of StatisticsUniversity of DelhiDelhiIndia

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