Reverse assignment: calibrating link cost functions and updating demand from traffic counts and time measurements

Abstract

In the literature, various models and procedures have been proposed for calibrating parameters of demand models or updating the demand values from traffic counts. Different models in terms of theoretical approaches have been used for congested and uncongested networks. Also for supply, models have been proposed for calibrating parameters of link cost functions. Link cost functions are calibrated separately from the demand. Congruence between the two calibrations is not guaranteed. This article proposes a unified formulation to obtain at the same time the parameters of link performance functions and the demand values (and/or the values of demand model parameters) of a static traffic assignment model. Model input consists of the a priori demand values, travel times measured on different links on the network, the link cost functions for each link category and the simulation model for user behaviour in path choice. Model output consists of the optimal demand, the parameters calibrated on link cost functions and the congruent flow on the links. The proposed model is thus called reverse assignment because the input is the output of a classical traffic assignment and the output is the input. The model is formulated as an optimization model for which the minimization of the distances between the a priori and optimal demand and modelled flows, measured and modelled travel times is sought. A heuristic optimization procedure for solving the model is proposed. The procedure considers the network that is congested and in each iteration of the optimization procedure a deterministic or a stochastic user equilibrium is solved. The problem of the existence of different local minimum points is discussed. There are major practical implications deriving from the solution of this problem. It allows transport models to be calibrated to simulate present and hypothetical scenario configurations prior to scenario implementation or within before–after planning procedures. The model and procedure are applied in a test and in a real system for different sets of parameters. The results confirm that if the unified formulation proposed is applied, the optimal demand and cost are better reproduced with respect to the traditional procedure where only demand or cost parameters are updated and the optimal point is strongly influenced by the a priori errors in the demand and link cost parameters.