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

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

Intelligent agent for formal modelling of temporal multi-agent systems

Software systems are becoming complex and dynamic with the passage of time, and to provide better fault tolerance and resource management they need to have the ability of self-adaptation. Multi-agent systems paradigm is an active area of research for modeling real-time systems. In this research, we have proposed a new agent named SA-ARTIS-agent, which is designed to work in hard real-time temporal constraints with the ability of self-adaptation. This agent can be used for the formal modeling of any self-adaptive real-time multi-agent system. Our agent integrates the MAPE-K feedback loop with ARTIS agent for the provision of self-adaptation. For an unambiguous description, we formally specify our SA-ARTIS-agent using Time-Communicating Object-Z (TCOZ) language. The objective of this research is to provide an intelligent agent with self-adaptive abilities for the execution of tasks with temporal constraints. Previous works in this domain have used Z language which is not expressive to model the distributed communication process of agents. The novelty of our work is that we specified the non-terminating behavior of agents using active class concept of TCOZ and expressed the distributed communication among agents. For communication between active entities, channel communication mechanism of TCOZ is utilized. We demonstrate the effectiveness of the proposed agent using a real-time case study of traffic monitoring system

Self-modifiable color petri nets for modeling user manipulation and network event handling

A Self-Modifiable Color Petri Net (SMCPN) which has multimedia synchronization capability and the ability to model user manipulation and network event (i.e. network congestion, etc.) handling is proposed in this paper. In SMCPN, there are two types of tokens: resource tokens representing resources to be presented and color tokens with two sub-types: one associated with some commands to modify the net mechanism in operation, another associated with a number to decide iteration times. Also introduced is a new type of resource token named reverse token that moves to the opposite direction of arcs. When user manipulation/network event occurs, color tokens associated with the corresponding interrupt handling commands will be injected into places that contain resource tokens. These commands are then executed to handle the user manipulation/network event. SMCPN has the desired general programmability in the following sense: 1) It allows handling of user manipulations or pre-specified events at any time while keeping the Petri net design simple and easy. 2) It allows the user to customize event handling beforehand. This means the system being modeled can handle not only commonly seen user interrupts (e.g. skip, reverse, freeze), the user is free to define new operations including network event handling. 3) It has the power to simulate self-modifying protocols. A simulator has been built to demonstrate the feasibility of SMCPN

Analyzing safety and fault tolerance using time Petri nets

The application of time Petri net modelling and analysis techniques to safety-critical real-time systems is explored and procedures described which allow analysis of safety, recoverability, and fault tolerance. These procedures can be used to help determine software requirements, to guide the use of fault detection and recovery procedures, to determine conditions which require immediate miti gating action to prevent accidents, etc. Thus it is possible to establish important properties duing the synthesis of the system and software design instead of using guesswork and costly a posteriori analysis

Modeling the Permeable Power of the Road on a Semaforized Crossing Using Petri Nets

With the growth in demand and the development of traffic over the last fifty years, the need for the introduction of Intelligent Transport Systems (ITS) is growing every day. With a modern approach they solve complex traffic problems. One modern approach is modeling the dynamics of Petri Nets. The Petri Nets is a powerful graphical and mathematical model for working with discrete systems. This paper describes how using a Petri Net can manage signaled intersections, assist in choosing the best alternative route, or manage an intersection at which an incident occurred. The research was carried out in a real traffic environment, at the intersection of Zagrebačka Road and Bistrička Road in the center of the city Sesvete, by modeling with coloured timed Petri Nets

Development of a Timed Coloured Petri Net Model for Time-of-Day Signal Timing Plan Transitions

In many countries, traffic signal control is one of the most cost effective means of improving urban mobility. Nevertheless, the signal control can be grouped into two principal classes, namely traffic-response and fixed-time. Precisely, a traffic response signal controller changes timing plan in real time according to traffic conditions while a fixed-time signal controller deploys multiple signal timing plans to cater for traffic demand changes during a day. To handle different traffic scenarios via fixed-time signal controls, traffic engineers determine such time-of-day intervals manually using one or two days worth of traffic data. That is, owing to significant variation in traffic volumes, the efficient use of fixed-time signal controllers depends primarily on selecting a number of signal timing plans within a day. In this paper, a Timed Coloured Petri Net (TCPN) formalism was explored to model transition between four signal timing plans of a traffic light control system such that a morning peak signal timing plan handles traffic demand between the hours of 6:00 am and 8:30 am, followed by afternoon I and afternoon II signal timing plans which handle traffic demands from 8:30 am to 3:00 pm and from 3:00 pm to 7:00 pm respectively, while the off peak plan handles traffic demands from 7:00 pm to 9:00 pm. Other hours of the day are ignored since they are characterized by low traffic demands. Keywords: Signal timing plan, Petri nets, Time-of-day, Model, Traffic, Fixed-time

Model predictive control of timed continuous petri nets

This thesis addresses the optimal control problem of timed continuous Petri nets. The theory of Model Predictive Control (MPC) is first discussed. Then continuous Petri nets (PN) are introduced as a powerful tool for modelling, simulation and analysis of discrete event/continuous systems. Their useful capabilities are studied. Finally, a macroscopic model based on PN as a tool for designing control laws that improve the behavior of traffic systems is given. The goal is to find an approach that minimizes the total delay of cars in an intersection by computing the switching sequence of the traffic lights. The simulation results show that by using an MPC strategy to handle the variability of traffic conditions, the total delay is dramatically reduced