Transport Modeling

Transport Modeling

In recent times, the world is experiencing a sharp increase in traffic and hence mathematical traffic modeling is needed more than ever. This is very clear in Sonoma and Santa Cruz Counties that are right in our vicinity and can serve as models for other urban regions. These counties are both facing an excess of traffic due to a variety of factors that include the growth of the wine industry and the community, and the increasing congestion caused by commuting to and from the bay area specifically from San Francisco and Silicon Valley. We are not only concerned with the overall growth of congestion and pollution, but also with understanding if and how it impacts various sub-communities in these counties. In both counties, their leaders are looking to develop policies and incentives to mitigate the environmental and health impacts and improve the transportation efficiency. It is then crucial to locate the regions that are mostly affected by emissions caused by traffic to develop effective and equitable solutions. This requires the development of an effective predictive simulation tool. Traffic modeling is extensively found in several academic fields including Numerical Analysis, Optimization, Reinforcement learning and Robotics with the usage of autonomous vehicles. We will be taking a numerical analysis approach and utilize partial differential equations as we are interested in exploring the predictive capability of PDE based traffic models.