Path-Based Dynamic User Equilibrium Model with Applications to Strategic Transportation Planning

Abstract

This study proposes an analytical capacity constrained dynamic traffic assignment (DTA) model along with an efficient path-based algorithm. The model can be applied to analyzing dynamic traffic demand management (TDM) strategies, but its specific feature is allowing for an evaluation of advanced traveler information systems (ATIS) within the strategic transportation planning framework. It is an extension of a former DTA model, where each link is given an infinite capacity and is assumed to be completely traversed inside any time interval it is reach by a path. Thereby, the length of time intervals should be very longer than the link travel times, and the link capacity constraints are overlooked. The paper rests on three key ideas to overcome these restrictions: (1) adding path-link fraction variables to the base model, allowing path flows to spread out over time intervals on long links; (2) uniformly dividing each link into smaller parts (segments), so that each part is more likely to be traversed inside a time interval; (3) imposing a dynamic penalty function on each link, thereby the capacity constraint can be included. The proposed DTA algorithm decomposes the augmented model in terms of origin-destination (OD) pairs and departure time intervals, and utilizes a dynamic column generation technique for generating active paths between the OD pairs. The optimal solution to a one-link network demonstrates that the model is able to approximate the dynamic flow propagation over a link with sensible accuracy. Besides, investigation of the results for a small test network reveals that the algorithm performs very well in computing temporal link flows and queuing delays. Finally, numerical experiments on a real life network indicate that the algorithm converges sufficiently fast and provides path information for each time interval. The network is further used to show the algorithm is capable of assessing a dynamic TDM strategy as well as an ATIS system.