B-Dynamic: An Efficient Algorithm for Dynamic User Equilibrium Assignment in Activity-Travel Networks

Multi-dimensional choice in DTA for example, a combined model of activity location, time of participation, duration, and route choice decisions results in exponentially increasing choice alternatives. Any efficient algorithm for solving the multi-dimensional DTA problem must avoid enumeration of alternatives. In this paper an algorithm that does not enumerate paths is presented. The algorithm is a novel extension of Algorithm B (Dial 2006) to dynamic networks and hence referred to as Algorithm B-Dynamic. The DTA model proposed here uses a point queue model for traffic propagation that reduces computational complexity. The activity participation decision dimensions are incorporated through utility functions which are a linear function of duration and schedule delay (early or late arrival penalty). Numerical examples are then presented to illustrate both the steps of the algorithm and its’ capabilities. Overall, the algorithm performed well for up to medium-sized networks. Further, the algorithm scales fairly well with increasing demand levels. ∗The first author is affiliated with the Department of Civil Engineering, Indian Institute of Technology, Madras, Chennai 600032, India and the second author is affiliated with the School of Civil Engineering, Purdue Univerisity, West Lafayette, IN 47907, U.S.A. Part of the work was carried out when the authors were at the Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, U.S.A. The email addresses of the authors are, respectively, [email protected], and [email protected].