Optimization of Traffic Signal Settings by Mixed-Integer Linear Programming

Setting traffic signals in a signal-controlled street network involves the determination of cycle time, splits of green time, and offsets. Part I of this paper considers the network coordination problem, i.e., given a common cycle lime and green splits at each intersection, determine offsets for all signals. Part II considers the more general synchronization problem, i.e., determine simultaneously all the control variables for the network including offsets, splits, and cycle time. In Part I, a link performance function is developed to express the loss incurred by platoons traveling through a signal-controlled intersection us a function of link offset. Integer variables enter the formulation because of the periodicity of the traffic lights: The algebraic sum of the offsets around any closed loop of the network must equal an integral number of cycle limes. The optimization problem is formulated as a mixed-integer linear program and a test network is solved by branch-and-bound techniques using IBM's MPSX package.