Development of a Combined Traffic Signal Control-Traffic Assignment Model

Having recognized the mutual interaction that exists between traffic signal control and route choice behavior, this paper considers the traffic assignment problem for a traffic signal controlled network. The interaction is characterized by (1) the effects of delay, due to traffic signals, on route choice, and (2) the influence of the resulting traffic assignment, due to the changes in route selection, on the timing of traffic signals. In this paper Webster’s method for calculating green splits and the HCM delay model are used to develop a link performance function that implicitly produces optimal signal settings for the arriving traffic volumes. This link-performance function is then used in an assignment procedure to develop a combined traffic signal control/traffic assignment model. The model provides simultaneous solution of the traffic signal control problem and the traffic assignment problem. The result is a set of signal settings that optimally matches the assigned traffic flows. The combined model results in a non-convex problem which produces multiple equilibria. A modification of Wardrop’s two principles is proposed to produce an assignment which converges to a single solution.