Continuous PEPA queues: individual behaviour in continuous queueing networks
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Tracking Control of Join-Free Timed Continuous Petri Net Systems under Infinite Servers Semantics
Discrete Event Dynamic Systems
On Controllability of Timed Continuous Petri Nets
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Basic Server Semantics and Performance Monotonicity of Continuous Petri Nets
Discrete Event Dynamic Systems
Automatica (Journal of IFAC)
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Performance control of Markovian Petri nets via fluid models: a stock-level control example
CASE'09 Proceedings of the fifth annual IEEE international conference on Automation science and engineering
On reachability in autonomous continuous Petri net systems
ICATPN'03 Proceedings of the 24th international conference on Applications and theory of Petri nets
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
How might petri nets enhance your systems biology toolkit
PETRI NETS'11 Proceedings of the 32nd international conference on Applications and theory of Petri Nets
On fluidization of discrete event models: observation and control of continuous Petri nets
Discrete Event Dynamic Systems
On the computational power of timed differentiable petri nets
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
Continuization of timed petri nets: from performance evaluation to observation and control
ICATPN'05 Proceedings of the 26th international conference on Applications and Theory of Petri Nets
Piecewise constant timed continuous PNs for the steady state estimation of stochastic PNs
Discrete Event Dynamic Systems
Optimal stationary behavior for a class of timed continuous Petri nets
Automatica (Journal of IFAC)
Steady-state performance evaluation of continuous mono-T-semiflow Petri nets
Automatica (Journal of IFAC)
Feasibility of piecewise-constant control sequences for timed continuous Petri nets
Automatica (Journal of IFAC)
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Petri nets are formalisms for the modeling of discrete event dynamic systems (DEDS). The integrality of the marking and of the transitions firing counters is a clear reflection of this. To reduce the computational complexity of the analysis or synthesis of Petri nets, two relaxations have been introduced at two different levels: (1) at net level, leading to continuous net systems; (2) at state equation level, which has allowed to obtain systems of linear inequalities, or linear programming problems. These relaxations are mainly related to the fractional firing of transitions, which implies the existence of non-integer markings. We give an overview of this emerging field. It is focused on the relationship between the properties of (discrete) PNs and the corresponding properties of their continuous approximation. Through the interleaving of qualitative and quantitative techniques, surprising results can be obtained from the analysis of these continuous systems. For these approximations to be "acceptable", it is necessary that large markings (populations) exist. It can also be seen, however, that not every populated net system can be continuized. In fact, there exist systems with "large" populations for which continuation does not make sense. The possibility of expressing nonlinear behaviors may lead to deterministic continuous differential systems with complex behaviors.