A gradient projection algorithm for side-constrained traffic assignment

Standard static traffic assignment models do not take into account the direct effects of capacities on network flows. Separable link performance functions cannot represent bottleneck and intersection delays, and thus might load links with traffic volumes, which far exceed their capacity. This work focuses on the side-constrained traffic assignment problem (SCTAP), which incorporates explicit capacity constraints into the traffic assignment framework to create a model that deals with capacities and queues. Assigned volumes are bounded by capacities, and queues are formed when capacity is reached. Delay values at these queues are closely related to Lagrange multipliers values, which are readily found in the solution. The equilibrium state is defined by total path travel times, which combine link travel times and delays at bottlenecks and intersections for which explicit capacity constraints have been introduced. This paper presents a new solution procedure for the SCTAP based on the inner penalty function method combined with a path-based adaptation of the gradient projection algorithm. This procedure finds a solution at the path level as well as at the link level. All intermediate solutions produced by the algorithm are strictly feasible. The procedure used to ensure that side-constraints are not violated is efficient since it is only performed on constrained links that belong to the shortest path.