A Class of Mixed Markov Processes and Their Application in Teletraffic Theory

We introduce and constructively define a class of mixed homogeneous Markov processes which, in addition to a discrete component, also contain a continuous evolving component. A system of differential equations and boundary conditions is derived for state densities and state probabilities of this process. An existence theorem is proved for the limit distribution. These stochastic processes are applied to some problems of teletraffic theory.