Traffic signals can be synchronized so that a car, starting at one end of a main artery and traveling at preset 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. Ordinarily, the bandwidth in each direction is single (not split into 2 or more intervals within a cycle). This research formulates the arterial problem as a mixed-integer linear program. Several variants are also formulated. A branch and bound algorithm is developed to solve the given mixed-integer linear program by solving a sequence of ordinary linear programs, and a 10-signal example is worked out. The synchronization of a network of signals problem is also formulated. The resulting program consists of the arterial programs for the individual streets plus a set of further constraints that arise because the streets connect together to form closed loops. The objective function used for the network program is a weighted sum of the bandwidths in each direction on each artery. A 7-signal example is worked out by branch and bound methods.
Abstract