Traffic assignment in a tolled network with heterogeneous values of time and budgets on toll

Abstract

A new network equilibrium problem was proposed for evaluating tolled traffic networks with heterogeneous values of time (VoT) and budgets on toll (BoT). Both parameters are important socio-economic characteristics primarily determined by the income level, trip purpose, etc., which directly affect the route choice and network flow pattern. Simpler models that embrace either of the attributes appeared a few times in the literature, but no study has been devoted to including both of them in an integrated model. This paper presents a mathematical programming model and method to characterize and solve this problem. In the well-known Frank-Wolfe algorithm framework, the core solution complexity lies in how to load travel demand into the network in an efficient manner. For tackling this difficulty, we developed a three-stage network loading procedure: (1) a bicriterion label-correcting algorithm finds all nondominated paths in the first stage; (2) a Graham scan algorithm is used to quickly identify all extreme nondominated paths in the second stage; (3) a constrained parametric algorithm is used to assign appropriate demand proportions to all eligible extreme nondominated paths. The numerical result derived from an illustrative example clearly shows how heterogeneous BoT and VoT reshape the network flow pattern from the simple case characterized merely by user equilibrium.

Keywords:

• Network equilibrium
• traffic demand
• heterogeneity
• value of time
• budget on toll