Rational Processes Related to Communicating Markov Processes

Journal of Applied Probability - Tập 49 Số 1 - Trang 40-59 - 2012
Peter Buchholz1, Miklós Telek2
1Universität Dortmund
2Budapest Univ. of Technology & Economics

Tóm tắt

We define a class of stochastic processes, denoted as marked rational arrival processes (MRAPs), which is an extension of matrix exponential distributions and rational arrival processes. Continuous-time Markov processes with labeled transitions are a subclass of this more general model class. New equivalence relations between processes are defined, and it is shown that these equivalence relations are natural extensions of strong and weak lumpability and the corresponding bisimulation relations that have been defined for Markov processes. If a general rational process is equivalent to a Markov process, it can be used in numerical analysis techniques instead of the Markov process. This observation allows one to apply MRAPs like Markov processes and since the new equivalence relations are more general than lumpability and bisimulation, it is sometimes possible to find smaller representations of given processes. Finally, we show that the equivalence is preserved by the composition of MRAPs and can therefore be exploited in compositional modeling.

Từ khóa


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Thông tin
Thông tin xuất bản

Journal of Applied Probability

Tập 49 Số 1

40-59

Thông tin tác giả