Using math to alleviate traffic jams
Washington: A new study proposes a mathematical model of vehicular traffic based on the study of a moving bottleneck caused by a slow-moving vehicle within the flow of cars.
Mathematical approaches to study traffic are usually based on the speed, density and flow of vehicles on a given roadway.
The effect of moving bottlenecks on flow of traffic is an important factor in evaluating travel times and traveling paths for commuters.
The study conducted by Corrado Lattanzio, Amelio Maurizi and Benedetto Piccoli provides a fully coupled, multi-scale model in which the microscopic position of a single car is taken together with the macroscopic car density on the road.
In the model, the dynamics of a moving bottleneck caused by a slow-moving vehicle on a street are used to study the effects of disruptions on the flow of traffic.
Mathematically, the problem is solved using the fractional step method. In successive time steps, a PDE (partial differential equation) is first solved for the density of traffic and then the ODE (ordinary differential equation) is solved for the position of the slow-moving vehicle.
By solving the bottleneck problem in a coupled fashion, better transportation designs can be made in anticipation of such inevitable traffic congestion.
The study is published this month in the SIAM Journal.
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