Optimization of area traffic control for equilibrium network flows

A bilevel programming approach is used to tackle an optimization problem for area traffic control and equilibrium flows. The signal timing plan is defined by common cycle time, and by starts and durations of greens. The system performance index is defined as the sum of a weighted linear combination of rate of delay and number of stops per unit time for all traffic streams, which is evaluated by the traffic model from TRANSYT. User equilibrium traffic assignment is formulated as a variational inequality problem. Approximate mathematical expressions for various components of the performance index and the average delay to a vehicle at the downstream junction in the TRANSYT model for both undersaturated and oversaturated links have been derived. For a locally optimal search, the gradient projection method is used in deciding whether feasible descent directions leading to a Karush–Kuhn–Tucker point, which is potentially a local optimum, can be identified. A global search heuristic is proposed in this paper by which successively better Karush–Kuhn–Tucker points can be found with reasonable computation effort. The mixed search procedure, including the locally optimal search and global search heuristic, is proposed. Encouraging results for Allsop and Charlesworth's network have confirmed that the approximately optimizing mixed search procedure in solving the area traffic control optimzation problem can achieve substantially better results than do the nonoptimizing calculations of mutually consistent signal timings and link flows.