Enhancing realism in modeling merge junctions in analytical models for system-optimal dynamic traffic assignment

The existing analytical system-optimal dynamic traffic assignment (SO-DTA) model formulated with the linear programming (LP) approach usually assumes system control over vehicles in the entire network. This property would give rise to unreasonable priorities at merge junctions that are sometimes physically impossible to realize for the given roadway configuration. In this paper, we demonstrate that models with and without considering the merge-priority ratio would exhibit very different traffic patterns and route-choice behavior. To realistically model traffic flow on a transportation network, one should properly distinguish the level of control by drivers, roadway geometry, and system providers. This paper also attempts to develop an LP module that explicitly considers the merge-priority ratio of a merge junction and can potentially be incorporated into the existing LP formulation of the SO-DTA problem based on the cell-transmission model. By more realistically modelling the behavior of vehicles at merge junctions, the obtained solution can be used as a benchmark to compare control strategies developed without explicitly considering the merge-priority ratio at merge junctions or strategies developed with heuristic approaches.