Achieving sustainable mobility is one of the challenges of the 21st century; a crucial goal is to mitigate traffic congestions while improving safety. The increasing needs for efficient traffic management strategies and for efficient, reliable and safe traffic infrastructures is changing the point of view on mathematical models from bare simulation tools to sophisticated design and optimization tools. Moreover the attention is rapidly moving the focus from centralized supervision strategies, to decentralized control strategies. In this paper we present a modular microscopic mathematical model for heterogeneous vehicular traffic on road networks, able to describe vehicles interactions with the network infrastructure (roads, traffic lights, etc.) and with other vehicles according to the well known potential fields approach. The modeling tool is able to capture different vehicles interactions and traffic phenomena such as queues, overtaking and car crashes. The obtained modeling tool has a strong control-oriented and optimization-oriented characterization and appears promising for traffic supervision and control design and for addressing optimization problems when designing the traffic infrastructure.
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