Modelagem e sincronização de sistemas a eventos discretos temporizados: aplicação ao tráfego urbano na coordenação de semáforos

Abstract

This work deals with the modeling and optimization for the synchronism of event-oriented systems, through Tropical algebra. The problems are contextualized through the application of synchronism in urban traffic light networks. Discrete event modeling has applications beyond the context of urban traffic, other systems where synchronization in resource sharing is desired, as well as an example of manufacturing systems. The control of green times at traffic lights is optimized according to the traffic demand matrix. From the results obtained in the optimization, which minimally guarantee the flow demands, we then deal with the sequencing of the phases and the synchronism among the subsystems. As a contribution, for the phase sequencing stage, it was proposed a metric capable of quantifying the level of timing plans for coordination of traffic lights in urban traffic networks, according to their flow demands. The objective function that calculates the system's synchronism value was compared with the results processed in the SEDT urban traffic simulator and demonstrated a correlation with the more realistic simulation. In optimizing the search for the best time plans, a heuristic is proposed, which performs the search by evaluating the combination between the pairs of adjacent intersections. The algorithm entitled Optimization of the Best Closers obtained superior performance in the simulations when compared with two other optimization algorithms. Contributions are also proposed by a package, the Tropical Lexicographic Synchronization Optimization, which calculates a vector capable of synchronizing state transitions according to a list of priorities. The solution for the optimization of synchronism operates the problem lexicographically, solving each sub-problem individually, obtaining the local solution through fractional tropical programming. The algorithms (pseudo-codes) and the codes of their implementations in free computational language are presented. Numerical examples have been developed and demonstrate the implementation of the methods. Larger cases demonstrated an improvement in the use of tropical lexicographic policy for synchronizing urban traffic systems coordination.