Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 3, Pages 397-410
On the calculation of steady-state loss probabilities in the queue
1Ukrainian National Academy of Sciences, Institute of Cybernetics, 40 Prospekt Glushkova, Kiev 252207 , Ukraine
2University of North London, School of Mathematical Sciences, Holloway Road, London N7 8DB, UK
Received 1 March 1994; Revised 1 June 1994
Copyright © 1994 Igor N. Kovalenko and J. Ben Atkinson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper considers methods for calculating the steady-state loss probability
in the queue. A previous study analyzed this queue in discrete time
and this led to an efficient, numerical approximation scheme for continuous-time
systems. The primary aim of the present work is to provide an alternative approach by analyzing the queue; i.e., assuming that the service time
can be represented by a matrix-exponential distribution. An efficient computational scheme based on this method is developed and some numerical examples
are studied. Some comparisons are made with the discrete-time approach, and
the two methods are seen to be complementary.