Hybrid Petri net model of a traffic intersection in an urban network

Control in urban traffic networks constitutes an important and challenging research topic nowadays. In the literature, a lot of work can be found devoted to improving the performance of the traffic flow in such systems, by means of controlling the red-to-green switching times of traffic signals. Different techniques have been proposed and commercially implemented, ranging from heuristic methods to model-based optimization. However, given the complexity of the dynamics and the scale of urban traffic networks, there is still a lot of scope for improvement. In this work, a new hybrid model for the traffic behavior at an intersection is introduced. It captures important aspects of the flow dynamics in urban networks. It is shown how this model can be used in order to obtain control strategies that improve the flow of traffic at intersections, leading to the future possibility of controlling several connected intersections in a distributed way

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

About Dynamical Systems Appearing in the Microscopic Traffic Modeling

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The dynamics of these Petri nets are well-defined and may be described by a generalized matrix with a submatrix in the standard algebra with possibly negative entries, and another submatrix in the minplus algebra. When the dynamics is additively homogeneous, a generalized additive eigenvalue may be introduced, and the ergodic theory may be used to define a growth rate under additional technical assumptions. In the traffic example of two roads with one junction, we compute explicitly the eigenvalue and we show, by numerical simulations, that these two quantities (the additive eigenvalue and the growth rate) are not equal, but are close to each other. With this result, we are able to extend the well-studied notion of fundamental traffic diagram (the average flow as a function of the car density on a road) to the case of two roads with one junction and give a very simple analytic approximation of this diagram where four phases appear with clear traffic interpretations. Simulations show that the fundamental diagram shape obtained is also valid for systems with many junctions. To simulate these systems, we have to compute their dynamics, which are not quite simple. For building them in a modular way, we introduce generalized parallel, series and feedback compositions of piecewise linear concave dynamics.Comment: PDF 38 page

Petri Nets Models for Analysis and Control of Public Bicycle-Sharing Systems

International audienc

Hybrid Petri nets-based Flow modeling and application on hybrid system.

Flow management is necessary in several application areas, in the optimization of industrial production lines, in IT to manage data flows and in the automation of industrial systems. Physical systems in general consist of continuous processes interacting with discrete processes forming a hybrid dynamic system constituted by continuous dynamic type models and discrete events. The application of the hybrid Petri nets tool in the modeling, study and performance evaluation of these systems helps to analyze the dynamic properties by acting on the parameters and the structure of the models in order to evaluate their behavior. This work is focused on the application of this tool to model a material flow management system between a rotary kiln and a clinker cooler in a production line (cement process). The implementation of the modeling and the analysis of the results obtained by simulation on a software platform (Visual Object Net ++), aims to study industrial processes with mathematical tools and to follow their behavior on software, this allows us an optimal analysis of complex systems in dangerous environments, and to try practical and effective solutions by simple means before moving on to the implementation and programming of actions that require more expensive means

Survivability modeling for cyber-physical systems subject to data corruption

Cyber-physical critical infrastructures are created when traditional physical infrastructure is supplemented with advanced monitoring, control, computing, and communication capability. More intelligent decision support and improved efficacy, dependability, and security are expected. Quantitative models and evaluation methods are required for determining the extent to which a cyber-physical infrastructure improves on its physical predecessors. It is essential that these models reflect both cyber and physical aspects of operation and failure. In this dissertation, we propose quantitative models for dependability attributes, in particular, survivability, of cyber-physical systems. Any malfunction or security breach, whether cyber or physical, that causes the system operation to depart from specifications will affect these dependability attributes. Our focus is on data corruption, which compromises decision support -- the fundamental role played by cyber infrastructure. The first research contribution of this work is a Petri net model for information exchange in cyber-physical systems, which facilitates i) evaluation of the extent of data corruption at a given time, and ii) illuminates the service degradation caused by propagation of corrupt data through the cyber infrastructure. In the second research contribution, we propose metrics and an evaluation method for survivability, which captures the extent of functionality retained by a system after a disruptive event. We illustrate the application of our methods through case studies on smart grids, intelligent water distribution networks, and intelligent transportation systems. Data, cyber infrastructure, and intelligent control are part and parcel of nearly every critical infrastructure that underpins daily life in developed countries. Our work provides means for quantifying and predicting the service degradation caused when cyber infrastructure fails to serve its intended purpose. It can also serve as the foundation for efforts to fortify critical systems and mitigate inevitable failures --Abstract, page iii