The Synchronization of Traffic Signals by Mixed-Integer Linear Programming

Traffic signals can be synchronized so that a car, starting at one end of a main artery and traveling at preassigned speeds, can go to the other end without stopping for a red light. The portion of a signal cycle for which this is possible is called the bandwidth for that direction. A mixed-integer linear program is formulated for the following arterial problem: Given (1) an arbitrary number of signals, (2) the red-green split at each signal, (3) upper and lower limits on signal period, (4) upper and lower limits on speed between adjacent signals, and (5) limits on change in speed, find (1) common signal period, (2) speeds between signals, and (3) the relative phasing of the signals, in order to maximize the sum of the bandwidths for the two directions. Several variants of the problem are formulated, including the problem of synchronizing a network of signals. Branch-and-bound algorithms are developed for solving the mixed-integer linear programs by solving sequences of ordinary linear programs. A 10-signal arterial example and a 7-signal network example are worked out.