Convergence of Traffic Assignments: How Much is Enough?

Abstract

Daily traffic assignments to a large-scale road network are described for build and no-build scenarios to evaluate the addition of two proposed ramps between I-295 and SR-42 in the New Jersey part of the Delaware Valley region. The road network consists of 39,800 links connecting 1,510 zones. The user-equilibrium traffic-assignment problem was solved with a new algorithm called origin-based assignment (OBA), which can achieve highly converged solutions with reasonable computing effort. Following a description of the user-equilibrium traffic-assignment problem and the OBA algorithm, the stability of link-flow differences between the two scenarios in the vicinity of the proposed ramps are examined over a broad range of assignment convergence levels. Then, link-flow differences over this range of convergence levels are compared to link-flow differences between two very highly converged solutions. Examination of the findings reveals, in the writers’ view, that a relative gap of 0.01% (0.0001) is required to ensure that the traffic assignments are sufficiently converged to achieve link-flow stability. These convergence levels are then interpreted in terms of the number of Frank-Wolfe iterations needed to achieve comparable relative gaps as well as the computational effort required.