Realistic Off-Ramp Coupling Conditions for Macroscopic Highway Network Models

Abstract

Transportation systems are among the critical infrastructures in every society. In order to design robust and reliable transportation networks, one needs to have a solid understanding of the behavior of the traffic flow in these networks. Many studies have been conducted to describe, control and predict the traffic flow on the networks. However, there are still some shortcomings in the existing literature that need to be addressed. For example, there are currently no satisfactory macroscopic coupling models for off-ramps on the highways. Specifically, existing models have fundamental modeling shortcomings, and model-fitting and validation of coupling models with traffic data have received little attention. To this end, this thesis will address some of the existing gaps in the literature of macroscopic traffic flow modeling by developing new coupling conditions for off-ramps on highways. This dissertation contributes to the existing literature in the following aspects: modeling, analysis, and validation with data. From a modeling point of view, there are two sets of coupling conditions in the literature for the off-ramp: FIFO (First In, First Out) and non-FIFO. Under the classical FIFO coupling conditions, a clogged off-ramp yields zero flux through the junction. Clearly, on multi-lane highways this is unrealistic, as a queue forming from the off-ramp will generally be restricted to the right-most lane, and vehicles that do not wish to exit can pass the queue. Moreover, the issue with the non-FIFO coupling conditions is that they lead to spurious re-routing of vehicles. To remedy these issues, we develop a new coupling model by using a vertical queue at the junction. The vertical queue keeps track of the excess vehicles of a certain type (exiting vs.~non-exiting) that may join the congested traffic by more than the other vehicle type does. From the analysis point of view, the introduction of the vertical queue as well as the requirement of the model to preserve the split ratios, lead to some differences from the existing models in the literature that renders proving the well-posedness of the model a non-trivial task. In this dissertation, we undertake this task and establish the well-posedness of the model. Specifically, we show that there exists a unique solution that is continuously dependent on the initial data. Finally, we use the data generated from a microsimulator to validate our model and compare it with the existing models. Specifically, we establish micro-simulation representations of the off-ramp scenarios, and describe how to systematically extract macro quantities from the results of the microsimulator. Then, we compare the results of the macroscopic models with the macro quantities extracted from the microsimulator.