2015/09/21 by Giacomo Como, Como, Giacomo, Enrico Lovisari +3 · 2 citations
Engineering · Social Sciences · #FOS: Mathematics #Optimization and Control (math.OC) #Traffic Prediction and Management Techniques #Traffic control and management #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.1509.06189
openalex publication_date 2015/09/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA)\nproblem to design optimal traffic flow controls for freeway networks as modeled\nby the Cell Transmission Model, using variable speed limit, ramp metering, and\nrouting. We consider two optimal control problems: the DTA problem, where\nturning ratios are part of the control inputs, and the Freeway Network Control\n(FNC), where turning ratios are instead assigned exogenous parameters. It is\nknown that relaxation of the supply and demand constraints in the cell-based\nformulations of the DTA problem results in a linear program. However, solutions\nto the relaxed problem can be infeasible with respect to traffic dynamics.\nPrevious work has shown that such solutions can be made feasible by proper\nchoice of ramp metering and variable speed limit control for specific traffic\nnetworks. We extend this procedure to arbitrary networks and provide insight\ninto the structure and robustness of the proposed optimal controllers. For a\nnetwork consisting only of ordinary, merge, and diverge junctions, where the\ncells have linear demand functions and affine supply functions with identical\nslopes, and the cost is the total traffic volume, we show, using the maximum\nprinciple, that variable speed limits are not needed in order to achieve\noptimality in the FNC problem, and ramp metering is sufficient. We also prove\nbounds on perturbation of the controlled system trajectory in terms of\nperturbations in initial traffic volume and exogenous inflows. These bounds,\nwhich leverage monotonicity properties of the controlled trajectory, are shown\nto be in close agreement with numerical simulation results.\n