Computational aspects of the workload distribution in the MMPP/GI/1 queue

Author

Jean-Marie, Alain ; Liu, Zhen ; Nain, Philippe ; Towsley, Don

Author_Institution

Inst. Nat. de Recherche en Inf. et Autom., Sophia Antipolis, France

Volume

16

Issue

5

fYear

1998

fDate

6/1/1998 12:00:00 AM

Firstpage

640

Lastpage

652

Abstract

We show how the analysis of Markov modulated rate processes can be used to address the problem of computing the distribution of W, the stationary workload in the MMPP/GI/1 queue. Using the results of papers by Anick et al. (1982); Mitra (1988); and Elwalid et al. (1991), we present the decomposition properties of the Laplace transform of W and efficient computational algorithms for computing its distribution. The techniques are also applied to compute the bounds on the distribution of W developed by Liu et al. (see JACM, vol.44, no.2, p.366-94, 1997). Numerical results illustrating the usefulness of the methods are given for the case of the superposition of independent, nonidentical sources

Keywords

Markov processes; computational complexity; matrix algebra; modulation; queueing theory; statistical analysis; ATM network; Laplace transform; MMPP/GI/1 queue; Markov modulated rate processes; admission control; computational complexity; decomposition properties; distribution bounds; efficient computational algorithms; independent nonidentical sources superposition; matrices; stationary workload distribution; Admission control; Asynchronous transfer mode; Distributed computing; Helium; Laplace equations; Quantum computing; Queueing analysis; Stochastic processes; Switches; Traffic control;

fLanguage

English

Journal_Title

Selected Areas in Communications, IEEE Journal on

Publisher

ieee

ISSN

0733-8716

Type

jour

DOI

10.1109/49.700902

Filename

700902