A mathematical programming based approach to macroscopic traffic assignment in a dynamic network with queues

The traffic networks within most medium to large urban areas experience traffic flows and/or controls, which lead to complex traffic dynamics, such as oversaturation queues, en-route re-routing of traffic, changes in signal timings, incidents, or sometimes even gridlock. Most of the traffic assignment methodologies that have been utilized to date to examine such networks, however, either have been predominately static in nature or have only approximated the full dynamics that are present in these networks. In contrast, some of the traffic simulation models that have attempted to better capture some of these operational dynamic characteristics have needed to ignore some finer elements of the dynamic routing aspects of the problem.;This thesis presents and demonstrates an alternative mathematical programming solution approach to dealing with queues in the dynamic traffic assignment problem. This new alternative will be referred to as the DYNAMIC model for short. The new approach performs a macroscopic network equilibrium analysis, similar to most traditional transportation planning oriented network equilibrium methods, but is responsive to operational network dynamics in a fashion that has traditionally only been observed in traffic engineering oriented simulation models. The proposed approach is a complement to the INTEGRATION model, which is foremast a highly detailed traffic simulation model, but which also provides dynamic traffic assignment capabilities in a fashion that has traditionally only been present in transportation planning models.;The model solves the dynamic traffic assignment problem using a tri-level programming technique. In the first level, new alternate minimum routes to traverse the network are found. At the second level, the proportion of vehicles that should utilize these alternative routes is solved. At the third level, the routes that vehicles utilize and the proportions in which vehicles utilize these routes are held constant, and a convergent solution between the resulting link travel times and the associated arrival time-lags at subsequent downstream links is solved.;The results from example networks show that the growth and decay of queues, and the spill back of traffic at capacity bottlenecks or incident sites can be modelled very accurately, and that the resulting diversion of traffic to alternative routes is being estimated appropriately in terms of both its timing and its magnitude. It is also shown that the model converges to the static assignment model solution when the time slice is set to be sufficiently long for the traffic flows to arrive at their destinations within the same time slice during which they departed.;The design of the algorithm at the core of the model is sufficiently general to make it possible for the algorithm to eventually deal with dynamic assignment problems for any large network even though at present the algorithm's implementation on a desktop computer of a network with 15 links for a simulation period of 90 minutes requires an execution time of 5 minutes.