The solution of certain two-dimensional Markov models
Advances in Applied Probability1982Vol. 14(2), pp. 295–308
Citations Over TimeTop 17% of 1982 papers
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.
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