Modelling and controlling traffic behaviour with continuous Petri nets

Traffic systems are discrete systems that can be heavily populated. One way of overcoming the state explosion problem inherent to heavily populated discrete systems is to relax the discrete model. Continuous Petri nets (PN) represent a relaxation of the original discrete Petri nets that leads to a compositional formalism to model traffic behaviour. This paper introduces some new features of continuous Petri nets that are useful to obtain realistic but compact models for traffic systems. Combining these continuous PN models with discrete PN models of traffic lights leads to a hybrid Petri net model that is appropriate for predicting traffic behaviour, and for designing trac light controllers that minimize the total delay of the vehicles in the system

Performance Evaluation of Road Traffic Control Using a Fuzzy Cellular Model

In this paper a method is proposed for performance evaluation of road traffic control systems. The method is designed to be implemented in an on-line simulation environment, which enables optimisation of adaptive traffic control strategies. Performance measures are computed using a fuzzy cellular traffic model, formulated as a hybrid system combining cellular automata and fuzzy calculus. Experimental results show that the introduced method allows the performance to be evaluated using imprecise traffic measurements. Moreover, the fuzzy definitions of performance measures are convenient for uncertainty determination in traffic control decisions.Comment: The final publication is available at http://www.springerlink.co

How can macroscopic models reveal self-organization in traffic flow?

In this paper we propose a new modeling technique for vehicular traffic flow, designed for capturing at a macroscopic level some effects, due to the microscopic granularity of the flow of cars, which would be lost with a purely continuous approach. The starting point is a multiscale method for pedestrian modeling, recently introduced in Cristiani et al., Multiscale Model. Simul., 2011, in which measure-theoretic tools are used to manage the microscopic and the macroscopic scales under a unique framework. In the resulting coupled model the two scales coexist and share information, in the sense that the same system is simultaneously described from both a discrete (microscopic) and a continuous (macroscopic) perspective. This way it is possible to perform numerical simulations in which the single trajectories and the average density of the moving agents affect each other. Such a method is here revisited in order to deal with multi-population traffic flow on networks. For illustrative purposes, we focus on the simple case of the intersection of two roads. By exploiting one of the main features of the multiscale method, namely its dimension-independence, we treat one-dimensional roads and two-dimensional junctions in a natural way, without referring to classical network theory. Furthermore, thanks to the coupling between the microscopic and the macroscopic scales, we model the continuous flow of cars without losing the right amount of granularity, which characterizes the real physical system and triggers self-organization effects, such as, for example, the oscillatory patterns visible at jammed uncontrolled crossroads.Comment: 7 pages, 7 figure

A fully-discrete-state kinetic theory approach to traffic flow on road networks

This paper presents a new approach to the modeling of vehicular traffic flows on road networks based on kinetic equations. While in the literature the problem has been extensively studied by means of macroscopic hydrodynamic models, to date there are still not, to the authors' knowledge, contributions tackling it from a genuine statistical mechanics point of view. Probably one of the reasons is the higher technical complexity of kinetic traffic models, further increased in case of several interconnected roads. Here such difficulties of the theory are overcome by taking advantage of a discrete structure of the space of microscopic states of the vehicles, which is also significant in view of including the intrinsic microscopic granularity of the system in the mesoscopic representation.Comment: 36 pages, 10 figure