Abstract
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.
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Breuer, L. On Markov-Additive Jump Processes. Queueing Systems 40, 75–91 (2002). https://doi.org/10.1023/A:1017996413769
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DOI: https://doi.org/10.1023/A:1017996413769