Freeway and Arterial Traffic Flow Simulation Analytically Embedded in Dynamic Assignment

This paper is an extension of earlier work on dynamic traffic assignment with an analytically embedded traffic flow simulation. Previously, a modified Greenshields’ speed-density relationship was used to derive a link travel time function that is monotonically increasing and convex with respect to density. It was recognized that this link travel time function is more applicable for freeway traffic than for arterial street traffic, where a large portion of travel times occurs at the nodes as a result of queueing. In this paper a version of the model is developed with explicit queueing links to simulate such traffic conditions on an arterial street network. The dynamic traffic assignment problem is formulated in a two-level optimization framework, separating the temporal and spatial variables into two problems. The lowerlevel problem represents an equilibrium traffic assignment model that solves the spatial variables subject to a set of feasible paths fixed by the temporal estimates from the upper-level problem. The upper-level problem determines the temporal variables by finding the minimum time-dependent travel times from the origin to all other nodes, assuming equilibrium traffic loads assigned from the previous lower-level problem to be fixed. A set of recursive equations is derived to compute the link traversal times that satisfy the first-in, first-out requirement. An iterative solution algorithm using small time steps with queueing links is developed to solve the proposed two-level dynamic traffic assignment problem. Results are also provided to show the effects of embedding a traffic simulation with explicit treatment of queues to capture traffic dynamics on arterial streets.