A modular Petri net to modeling and scenario analysis of a network of road traffic signals Michel dos Santos Soares a,n , Jos Vrancken b a Universidade Federal de Uberlˆ andia, P.O. Box 593, 38400-902 Uberlˆ andia, Brazil b Delft University of Technology, P.O. Box 5015, NL 2600 GA, Delft, The Netherlands article info Article history: Received 22 September 2011 Accepted 16 June 2012 Keywords: Petri nets Traffic signals control Linear logic Formal analysis Real time systems abstract The dynamic behavior of a group of traffic signals controlling a network of intersections is a complex discrete event system that can be modeled by Petri nets. The approach used in this paper proposes a components-based design, which increases modularity, reduces complexity and is a good practice according to modern Systems Engineering. The main system elements are specified based on the proposed Petri net component with time intervals associated to places. The specified models are simulated through the common token player algorithm, and formal analysis using invariants and theorem proving are applied to verify models’ soundness and to reason on specific scenarios. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction When designing distributed real-time systems for critical infrastructures, such as transportation and energy networks, system complexity is increased due to the large number of elements, strict real-time constraints, and reliability factors, as these systems involve human life. Therefore, it is necessary to use methods that are capable of addressing complexity and providing highly reliable solutions. Formal methods fulfill these require- ments, by allowing formal proofs of desirable behavior and validation of performance characteristics by simulations. In addi- tion, if a formal method features modular design and abstraction, then this contributes substantially to complexity reduction. A number of approaches have been used to model distributed real-time systems in general, and traffic control systems in particular. Finite State Machines (FSMs) have been used for modeling distributed real-time systems (Cassandras & Lafortune, 2006), but have the shortcoming of state explosion (Brave, 1993). Statecharts (Harel, 1987) extends state-machines by endowing them with orthogonality, depth, and synchronization. An approach to model urban traffic signal control using Statecharts was proposed in Huang (2006). Petri nets (Murata, 1989) are used in this paper. The choice is based on their modeling expressivity, their facilities for validation and verification activities, the availability of computer tools, and the range of available extensions. Petri nets are suitable to model distributed real-time systems because they offer representation of important situations commonly found in this kind of systems, including conflict situations, shared resources, synchronous and asynchronous communication, and precedence constraints. As a formal language, Petri nets allow formal checks of desirable properties. The formal analysis of a Petri net model can reveal design flaws (Girault & Valk, 2003). For instance, with reachability analysis it is possible to find out whether an unsafe state that could cause an accident can be reached. The extensions proposed in this paper to the basic Petri net model are useful to address complexity and model real-time constraints. Finally, there are a variety of computer-based tools that support the Petri net theory, by performing verification and simulation of models. 1.1. Literature review Petri nets are a well-known formalism applied in traffic control research, including air traffic control (Huang & Chung, 2011) and railway traffic control (Cheng & Yang, 2009). The core of this research is the application of Petri nets to road traffic control. With focus on only one intersection, Huang, Chung, and ChenSystems (2005) described the traffic signal control using timed color Petri nets. Soares and Vrancken (2007b) proposed an approach based on the application of Petri nets and theorem proving to formally analyze the properties of traffic signals controlling one road intersection. These works are based on Petri net models without explicitly adding time for each phase dura- tion. Considering networks of roads, one of the first applications of Petri nets for traffic signals control in urban networks was Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/conengprac Control Engineering Practice 0967-0661/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conengprac.2012.06.005 n Corresponding author. Fax: þ55 34 3239 4392. E-mail addresses: michel@facom.ufu.br, mics.soares@gmail.com (M. dos Santos Soares). Please cite this article as: dos Santos Soares, M., & Vrancken, J. A modular Petri net to modeling and scenario analysis of a network of road traffic signals. Control Engineering Practice (2012), http://dx.doi.org/10.1016/j.conengprac.2012.06.005 Control Engineering Practice ] (]]]]) ]]]–]]]