Abstract
Markov processes are an important ingredient in a variety of stochastic applications. Notable instances include queueing systems and traffic processes offered
to them. This paper is concerned with Markovian traffic, i.e., traffic processes
whose inter-arrival times (separating the time points of discrete arrivals) form a
real-valued Markov chain. As such this paper aims to extend the classical results
of renewal traffic, where interarrival times are assumed to be independent, identically distributed. Following traditional renewal theory, three functions are addressed: the probability of the number of arrivals in a given interval, the corresponding mean number, and the probability of the times of future arrivals. The
paper derives integral equations for these functions in the transform domain.
These are then specialized to a subclass,