Extension and Generalization of Newell's Simplified Theory of Kinematic Waves
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Flow of traffic on freeways and limited access highways can be represented as a series of kinemetic waves. Solutions to these systems of equations become problematic under congested traffic flow conditions, and under complicated (real-world) networks. A simplified theory of kinematics waves was previously proposed. Simplifying elements includes translation of the problem to moving coordinate system, adoption of bi-linear speed-density relationships, and adoption of restrictive constraints at the on- and off-ramps. However, these simplifying assumptions preclude application of this technique to most practical situations. This research explores the limitations of the simplified theory of kinematic waves. First this research documents a relaxation of several key constraints. In the original theory, priority was given to on-ramp merging vehicles so that they can bypass any queue at the merge. This research proposes to relax this constraint using a capacity-based weighted fair queuing (CBWFQ) merge model. In the original theory, downstream queue affects upstream traffic as a whole and exiting traffic can always be able to leave as long as it gets to the diverge. This research proposes that this diverge constraint be replaced with a contribution-based weighted splitting (CBWS) diverge model. This research proposes a revised notation system, permitting the solution techniques to be extended to freeway networks with multiple freeways and their ramps. This research proposes a generalization to permit application of the revised theory to general transportation networks. A generalized CBWFQ merge model and a generalized CBWS diverge model are formulated to deal with merging and diverging traffic. Finally, this research presents computational procedure for solving the new system of equations. Comparisons of model predictions with field observations are conducted on GA 400 in Atlanta. Investigations into the performance of the proposed CBWFQ and CBWS models are conducted. Results are quite encouraging, quantitative measures suggest satisfactory accuracy with narrow confidence interval.