Traffic modeling has been of interest to mathematicians since the 1950s. Research in the area has only grown as road traffic control presents an ever-increasing problem.
Generally, models for traffic flow in road networks are time-dependent and continuous, that is, they describe traffic by a continuum rather than as individual drivers or cars. These macroscopic models describe the temporal and spatial evolution of traffic density without predicting traffic patterns of individuals. In addition to macroscopic models based on continuous densities, microscopic approaches like particle models or cellular automata are also used to model traffic.
Traffic modeling has been of interest to mathematicians since the 1950s. Research in the area has only grown as road traffic control presents an ever-increasing problem.
Generally, models for traffic flow in road networks are time-dependent and continuous, that is, they describe traffic by a continuum rather than as individual drivers or cars. These macroscopic models describe the temporal and spatial evolution of traffic density without predicting traffic patterns of individuals. In addition to macroscopic models based on continuous densities, microscopic approaches like particle models or cellular automata are also used to model traffic.
Most existing continuous models consider unidirectional traffic; thus, the traffic density depends only on a single spatial dimension. The governing equations in this class of macroscopic models are inspired by gas dynamics equations.
A lot of recent work has focused on traffic intersections, which constitute a building block of larger road networks. Here, models generally aim to either minimize travel time of individual drivers, or maximize the total traffic flow at a given intersection.
Continue reading at Society for Industrial and Applied Mathematics (SIAM)
Image: Traffic at Song-shou and Song-chih Intersection in Taipei, Taiwan.
Image credit: Wikimedia Commons
