A dynamic traffic assignment model with traffic-flow relationships

Conventional traffic assignment methods assume that the origin-destination (OD) demand is uniformly distributed over time to estimate the traffic pattern. This assumption does not hold for modeling peak periods of congestion in which the OD demand is time varying. In this paper, we present a dynamic traffic assignment model with traffic-flow relationships based on a bi-level optimization framework. Our assignment variable is the number of vehicles present on a link during a time step, rather than traffic flow, which is used in static assignment. Using the modified Greenshields speed-density relationship, we derive a link-cost function that is monotonically nondecreasing and convex with respect to density. To capture traffic dynamics, we use short time-steps. The model prevents violations of the first-in-first-out (FIFO) condition using constraints on the distances moved by vehicles during each time step. A solution algorithm which resembles a Stackelberg leader-follower problem is presented, and numerical results from networks of different sizes demonstrate that the proposed model performs satisfactorily.