Adjustment of the link travel-time functions in traffic equilibrium assignment models

Abstract

The network calibration problem (NCP) consists of adjusting (or estimating) the parameters of the link travel-time functions in a congested traffic network via the use of traffic link counts and equilibrium costs in a set of origin–destination demand pairs. In this article, a mathematical program with equilibrium constraints (MPEC) is proposed to model this problem. The proposed model is called NCP(ρ) and supposes that the available information has been obtained in several different periods (each period is defined by a single origin–destination demand matrix). The existence of the solutions to the stated NCP(ρ) under weak conditions in the link travel-time functions is established, and a sensitivity analysis of these solutions is carried out. A column generation algorithm (CGA) is proposed to solve the NCP(ρ) model, using sensitivity analysis to prove that this algorithm converges to a local optimum of the MPEC problem. Finally, the special case of estimating the link travel-time functions in additive models when information is only available for a single period is analysed in a numerical study. In this case the NCP(ρ) model is overspecified, that is, it has an infinite number of solutions. For this reason we propose, as an alternative, estimating the congestion costs ψ in a subset of links, rather than estimating the parameterisation of the link travel-time functions ρ. This special case has been named the NCP(ψ) model. The numerical study has been carried out in small and medium-sized networks, with the objective of studying both the proposed MPEC models and the computational aspects of the CGA.