Formulation of the dynamic traffic assignment problem with an analytically embedded traffic model

Dynamic Traffic Assignment (DTA) has been identified as the backbone of the two major systems, Advanced Traffic Management Systems (ATMS) and Advanced Traveler Information Systems (ATIS), in the general Intelligent Transportation Systems (ITS) framework developed to make traveling quicker, easier, safer, and cleaner. The success of ATMS/ATIS depends greatly on DTA to provide timely and accurate estimates of current and future states of the traffic system. In this dissertation, a radically new approach is developed to solve the DTA problem. This approach analytically embeds a hydrodynamic flow model as a simulation into an optimization-based DTA framework. This is the first analytical DTA model where simulation equations are incorporated as constraints to move traffic that respect the first-in-first-out (FIFO) requirement in an optimization formulation for network assignment. It obviates the difficulty of imposing external FIFO constraints that may not be consistent or justified with observed or theoretical traffic flow behavior. A distinct feature of this approach is the use of traffic load (number of vehicles) as the assignment variable which results in convex travel time functions that are realistic for both uncongested and congested traffic conditions. Another unique feature of the framework is the use of small time-discretizations, with the theoretical correctness of the model improving with decreasing time step lengths.; Network assignment is accomplished for the time-dependent origin-destination demands based on a two-level optimization framework which fixes the incidence indicator between the time-dependent paths and their constituent links at one level and then assigns traffic similar to a static traffic assignment at the other level. Using this analytically embedded framework, four DTA models are developed in this dissertation to address different requirements in ATMS/ATIS. Specifically, it solves both user equilibrium and system optimal traffic assignments in the same analytical DTA framework. Traffic dynamics on freeways integrated together with arterial streets for both uncongested and congested traffic conditions are captured by a queuing version of the analytically embedded DTA model. The described solution algorithms look for off-line evaluation, but on-line applications such as short-term traffic prediction and route guidance have greater needs. Several dynamic rolling horizon DTA models are formulated according to the capability to re-route previously assigned vehicles. Solution procedures have been designed, implemented, and applied to various networks, including the Anaheim Testbed network, with considerable success.