Optimization of Traffic Behavior via Fluid Dynamic Approach

Abstract

Traffic regulation techniques for the optimization of car traffic flows in congested urban networks was considered. The approach used for the description of traffic flows is of fluiddynamic type. The main advantages of this approach, with respect to existing ones, can be summarized as follows. The fluid-dynamic models are completely evolutive, thus they are able to describe the traffic situation of a network at every instant of time. This overcomes the difficulties encountered by many static models. An accurate description of queues formation and evolution on the network is possible. The theory permits the development of efficient numerical schemes also for very large networks. This is possible since traffic at junctions is modelled in a simple and computationally convenient way (resorting to a linear programming problem). The performance analysis of the networks was made through the use of different cost functionals, measuring car average velocity weighted or not weighted with the number of cars moving on each road, the average travelling time, velocity variation, kinetic energy, etc. Exact analytical results were given for simple junctions of 1 ×2 and 2 × 1 type, and then used in order to simulate more complex urban networks. Moreover the problem of emergency vehicles transit has been treated. The problem has been faced choosing a route for emergency vehicles (not dedicated, i.e. not limited only to emergency needs) and redistributing traffic flows at junctions on the basis of the current traffic load in such way that emergency vehicles could travel at the maximum allowed speed along the assigned roads (and without blocking the traffic on other roads). All the optimization results have been obtained using a decentralized approach, i.e. an approach which sets local optimal parameters for each junction of the network. In future we aim to extend the optimization results to more general junctions and to explore global optimization techniques. In addition, the definition and optimization of functionals which take into account the emission and propagation of pollutants produced by cars might provide powerful technological tools to rationalize the design and use of public and private transportation resources, and to reduce unpleasant effects of urban traffic on the environment.

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