Traffic assignment and traffic control in general freeway-arterial corridor systems

We consider a general traffic corridor consisting of two subsystems of a freeway network and a surface street network. The two systems are coupled by access ramps to provide multiple alternative routes for drivers from their origins to destinations. Each ramp can be metered to influence flow distributions in such a way that some system performance index (e.g. total travel time) is optimized, provided that each driver chooses an individual minimum cost route in response to any given ramp control. In this article we first present a bilevel programming formulation of the traffic assignment and traffic control problem in the traffic corridor system. The lower-level problem represents a traffic equilibrium model involving explicitly ramp queuing, which predicts how drivers will react to any given on-ramp control pattern. The upper-level problem is to determine ramp metering rates that optimize a system performance criterion, taking into account drivers' route choice behavior. We also present a sensitivity analysis for the queuing network equilibrium problem. Explicit expression of the derivatives of equilibrium link flows and equilibrium ramp queuing times with respect to ramp metering rates is derived. A heuristic algorithm, using the derivative information from the sensitivity analysis, is developed to solve the proposed bilevel on-ramp traffic control problem. A numerical example is provided to illustrate the bilevel control model and the solution algorithm.