Hybrid modelling of transportation systems by means of Petri nets

A novel hybrid model for transportation systems is proposed, in which the functioning is represented via a continuous-time model whenever no changes in the traffic flow occur, whereas the changes in the system behaviour are modelled through a discrete event system coupled with the continuous-time system. Via the discrete-event part of the hybrid model, its continuous-time part is adapted according to the variation occurred in the system behaviour. The hybrid modelling methodology proposed is based on the use of a special class of Petri nets, the hybrid stochastic Petri nets (HSPN). These nets are composed of some discrete parts, and some continuous parts, so that a hybrid Petri net can be viewed as a combination of an usual (discrete) Petri net and a continuous Petri net, the 'fluid' version of usual timed Petri nets. The discrete part of the HSPN 'regulates' the continuous PN, which models the functioning of the transportation system. This results in the model reacting to any change to the current system behaviour by adapting the traffic parameters to the new state.

[1]  Antonella Ferrara,et al.  A new two-level model for multiclass freeway traffic , 1996 .

[2]  Stef Smulders,et al.  Control of freeway traffic flow by variable speed signs , 1990 .

[3]  Harold J Payne,et al.  MODELS OF FREEWAY TRAFFIC AND CONTROL. , 1971 .

[4]  V. Borkar,et al.  A unified framework for hybrid control , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[5]  Panos J. Antsaklis,et al.  Event identification in hybrid control systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[6]  Antonella Ferrara,et al.  Optimal control of freeways via speed signalling and ramp metering , 1997 .

[7]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[8]  Christos G. Cassandras,et al.  Introduction to the Modelling, Control and Optimization of Discrete Event Systems , 1995 .

[9]  A. Ferrara,et al.  Modelling freeway systems: a new traffic fundamental diagram , 1997 .

[10]  J. Quadrat,et al.  Asymptotic throughput of continuous timed Petri nets , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[11]  Semyon M. Meerkov,et al.  Feedback control of highway congestion by a fair on-ramp metering , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[12]  M. Branicky.  Topology of hybrid systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[13]  Steve Vestal,et al.  An implementation for hybrid continuous variable/discrete event dynamic systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[14]  Markos Papageorgiou,et al.  Applications of Automatic Control Concepts to Traffic Flow Modeling and Control , 1983 .