Hybrid Limits of Continuous Time Markov Chains

TitleHybrid Limits of Continuous Time Markov Chains
Publication TypeConference Paper
Year of Publication2011
AuthorsBortolussi L
EditorPalamidessi C, Riska A
Conference Name8th International Conference on Quantitative Evaluation of SysTems, QEST 2011
Pages3–12
Date Published8 September 2011
PublisherIEEE computer society
Conference LocationAachen
KeywordsContinuous Time Markov Chains, fluid approximation, limit theorems, mean field approximation, piecewise smooth dynamical systems., Stochastic modelling
Abstract

We consider the behaviour of sequences of Continuous Time Markov Chains (CTMC) based models of systems of interacting entities, for increasing population levels, in situations when some transitions of the system have rates that are discontinuous functions. This can happen, for instance, in presence of guarded actions. In this setting, standard deterministic approximation results do not apply. However, one can still derive a differential equation by syntactic means, de facto defining an hybrid (piecewise-smooth) dynamical system. We prove that the sequence of CTMC converges to the trajectories of this hybrid dynamical system, under (mild) regularity conditions on these limit trajectories.

Notes

Best paper award

DOI10.1109/QEST.2011.10