On Markov-additive jump processes

In 1995, Pacheco and Prabhu introduced the class of so-called

Markov-additive processes of arrivals in order to provide a general

class of arrival processes for queueing theory. In this paper, the

above class is generalized considerably, including time-inhomogeneous

arrival rates, general phase spaces and the arrival space being a

general vector space (instead of the finite-dimensional Euclidean

space). Furthermore, the class of Markov-additive jump processes

introduced in the present paper is embedded into the existing theory of

jump processes. The best known special case is the class of BMAP

arrival processes.