The solution of certain two-dimensional Markov models
- 1 March 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 14 (02) , 295-308
- https://doi.org/10.1017/s0001867800020450
Abstract
A class of two-dimensional birth-and-death processes, with applications in many modelling problems, is defined and analysed in the steady state. These are processes whose instantaneous transition rates are state-dependent in a restricted way. Generating functions for the steady-state distribution are obtained by solving a functional equation in two variables. That solution method lends itself readily to numerical implementation. Some aspects of the numerical solution are discussed, using a particular model as an example.Keywords
This publication has 1 reference indexed in Scilit:
- Two coupled processors: The reduction to a Riemann-Hilbert problemProbability Theory and Related Fields, 1979