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International Conference on Statistics, Combinatorics and Related Areas - 7th International Conference of the Forum for Interdisciplinary Mathematics
December 19-21, 2000
Indian Institute of Technology-Bombay
Mumbai, Maharastra, India

Organizers
Satya N. Mishra (University of South Alabama), Sanjeev V. Sabnis (IIT, Bombay)

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Some Combinatorial aspects of M/G/1 Type Queues
by
Gopal M. Nair
Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth 6845, Australia

Markov Chains of M/G/1 type arise extensively in the fields of teletraffic analysis and engineering.Neuts has shown that these models can be studied using a matrix genaralisation of embedded Markov chains. Recently there has been many papers devoted to development of efficient and relaible algorithms for the computation of the first passage distribution matrix, G, for M/G/1 type queue. In this paper we take a different approach to obtain the matrix G. We explore some combinatorial properties associated with G by expressing the events of interest as a set of integer compositions satisfying Ballot-type constraints. The matrix G is constructed using the recursive propeties of the set of integer compositions. The mathod will be applied to several special cases of M/G/1 type queues.

Date received: November 13, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafr-96.