Link State Relationships under Incident Conditions: Using a CTM-Based Linear Programming Dynamic Traffic Assignment Model
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Link State Relationships under Incident Conditions: Using a CTM-Based Linear Programming Dynamic Traffic Assignment Model

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    Urban transportation networks, consisting of numerous links and nodes, experience traffic incidents such as accidents and road maintenance work. A typical consequence of incidents is congestion which results in long queues and causes high travel time variability. In order to combat the negative effects due to congestion, various mitigation strategies have been proposed and implemented in the United States and worldwide. The effectiveness of these congestion mitigation strategies for incident conditions largely depends on the accuracy of information regarding network conditions. Therefore, an efficient and accurate procedure to determine the link states, reflected by flows and density over time, is essential to incident management. This research project constructs a user equilibrium Dynamic Traffic Assignment (DTA) model using linear programming (LP) that incorporates the Cell Transmission Model (CTM) to evaluate the temporal variation of flow and density over links, which accurately reflect the link states of a transportation network. The proposed model adopts a scheme of bi-level optimization in which the upper level program determines the flows over the network while the lower level program (CTM) propagates flows according to widely-accepted traffic flow theory. Encapsulation of the CTM equips the model with the capability of accepting inputs of incidents like duration and capacity reduction. Moreover, the proposed bi-level model is capable of handling multiple origin-destination (OD) pairs, which is a strength that most LP-based DTA models do not possess. By using this model, the temporal variation of flows over links can be readily evaluated and thus it can be used to predict the time-dependent link states. The results of numerical examples show that the flow pattern preserves the user equilibrium principle and satisfies the First-In-First-Out (FIFO) condition. The link-based encapsulation of CTM is able to temporally capture the queue between links and fully mimics the spillback within links.

    The flow pattern resultant from the proposed LP-DTA procedure can be transformed to density variation diagrams of links. These visualized density predictions provide insights to link state relationships by graphically describing the states of all the links of a transportation network. The impact of incidents on links can be reflected by their density and flow variations during and after the incidents. The results of the numerical examples, by isolating the effects of the incident, show that the parallel routes of a specific OD pair display the relationship of substituting for each other, which is consistent with general expectations. A closer examination over the density variations confirms the existence of a substitution relationship between the unshared links of the two routes connecting an OD pair. Quantitative information about the additional traffic on the diversion route in terms of amount and duration of diverted traffic is also obtained.

    Two levels of application of link state relationships are identified for real-world situations. Information about link states for different incident scenarios can be aggregated and mined to derive general patterns for the link state relationships. These patterns can be used as general guidance for incident management purposes. A microscopic level of application involves usage of flow and density predictions for a specific incident to determine which specific incident management strategy (e.g. opening the HOV lane to all traffic or changing signal timing) is most beneficial.

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