Traffic assignment and signal control in saturated road networks

This article presents a model and a procedure for determining traffic assignment and optimizing signal timings in saturated road networks. Both queuing and congestion are explicitly taken into account in predicting equilibrium flows and setting signal split parameters for a fixed pattern of origin-to-destination trip demand. The model is formulated as a bilevel programming problem. The lower-level problem represents a network equilibrium model involving queuing explicitly on saturated links, which predicts how drivers will react to any given signal control pattern. The upper-level problem is to determine signal splits to optimize a system objective function, taking account of drivers' route choice behavior in response to signal split changes. Sensitivity analysis is implemented for the queuing network equilibrium problem to obtain the derivatives of equilibrium link flows and equilibrium queuing delays with respect to signal splits. The derivative information is then used to develop a gradient descent algorithm to solve the proposed bilevel traffic signal control problem. A numerical example is included to demonstrate the potential application of the assignment model and signal optimization procedure.