Fluid limits of queueing networks with batches
ICPE '12 Proceedings of the 3rd ACM/SPEC International Conference on Performance Engineering
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
Mean-Field analysis of markov models with reward feedback
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Continuous approximation of collective system behaviour: A tutorial
Performance Evaluation
Fluid limit for the machine repairman model with phase-type distributions
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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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.