A DYNAMIC TRAFFIC ASSIGNMENT MODEL WITH TRAFFIC-FLOW RELATIONSHIPS

Conventional traffic assignment methods assume that the origin-destina tion (OD) demand is uniformly distributed over time to estimate the tr affic 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 relati onships based on a bi-level optimization framework. Our assignment var iable is the number of vehicles present on a link during a time step, rather than traffic flow, which is used in static assignment. Using th e modified Greenshields speed-density relationship, we derive a link-c ost function that is monotonically nondecreasing and convex with respe ct to density. To capture traffic dynamics, we use short time-steps. T he model prevents violations of the first-in-first-out (FIFO) conditio n using constraints on the distances moved by vehicles during each tim e step. A solution algorithm which resembles a Stackelberg leader-foll ower problem is presented, and numerical results from networks of diff erent sizes demonstrate that the proposed model performs satisfactoril y.