A trio of researchers in Italy has developed a mathematical model for a common cause of traffic jams, the slow-moving vehicle, such as a farm tractor or heavy truck, on a crowded highway. The team of Corrado Lattanzio and Amelio Maurizi from University of L’Aquila, with Benedetto Piccoli of Italy’s Institute in Applied Mathematics, published their findings in the January issue of the the SIAM Journal on Mathematical Analysis (paid subscription required).
Traffic flow models help design highways and influence the position of traffic lights, toll booths, tunnels, and overpasses. The models help relieve congestion in high traffic areas, reduce the risk of accidents, and manage safety and security of motorists.
Most of the earlier traffic flow models, however, looked at the individual vehicle independently from the surrounding flow of traffic. They use an ordinary differential equation (ODE) to determine the position of a single vehicle, with a partial differential equation (PDE) to model the flow of traffic.
Lattanzio’s team analyzed the bottleneck caused by an individual slow-moving vehicle in conjunction with the surrounding traffic. For this model, they connect the position of a single car or truck together with the overall density of vehicles on the road. Mathematically, they solve the problem by using a fractional step method. In successive steps, a PDE is first solved for the density of traffic and then the ODE is solved for the position of the slow-moving vehicle.
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Photo: Danielle Scott/Flickr
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