​Mark J. Panaggio

How should traffic signals be timed to allow traffic to flow efficiently? This simple question has perplexed traffic engineers since the advent of the traffic signal in the late 1800s.  When choosing the timing (duration of the green/yellow/red phases and the start time) for a stoplight at an intersection, there are many factors that one might consider: the traffic load, the distance from neighboring intersections, the number of lanes, the time of day, etc.  These factors in conjunction with the unpredictability of the arrival times of vehicles make optimizing traffic signals a challenging mathematical problem. However, in certain idealized cases optimal solutions can be found.  

 

For example, on a one-way street, the optimal timing scheme is called a green-wave.  In this scheme, a wave of green lights travels down the road at the speed of traffic travels so that once a vehicle reaches a green light, they will encounter green-lights exclusively and be able to proceed indefinitely without stopping.  Unfortunately, these solutions are not possible on two-way streets due to the competing demands of traffic in both directions.  In a recent paper with Bertrand Ottino-Löffler, Peiguang Hu, and Danny Abrams, we were able to determine the timing scheme that minizes the delays under idealized conditions (low traffic density,  constant traffic speed, evenly spaced lights).  I am interested in exploring how these results can be generalized.  Can optimal solutions be obtained for a grid of two-way streets? What about an arbitrary road network? How does the efficiency depend on the traffic density? Can the phase transition to a traffic jam be computed analytically?

 

In addition to this, I am also interested in investigating adaptive and self-organizing control schemes. In practice, traffic densities change over time, so fixed timing schemes will be inherently inefficient.  How can traffic signals timings intelligently adapt to fluctuating demands?  How can we guarantee that those adaptations lead to desirable states?  Answering these questions could lead to significant reductions in wasted fuel and time for commuters in urban and suburban environments.