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We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA)problem to design optimal traffic flow controls for freeway networks as modeledby the Cell Transmission Model, using variable speed limit, ramp metering, androuting. We consider two optimal control problems: the DTA problem, whereturning ratios are part of the control inputs, and the Freeway Network Control(FNC), where turning ratios are instead assigned exogenous parameters. It isknown that relaxation of the supply and demand constraints in the cell-basedformulations of the DTA problem results in a linear program. However, solutionsto the relaxed problem can be infeasible with respect to traffic dynamics.Previous work has shown that such solutions can be made feasible by properchoice of ramp metering and variable speed limit control for specific trafficnetworks. We extend this procedure to arbitrary networks and provide insightinto the structure and robustness of the proposed optimal controllers. For anetwork consisting only of ordinary, merge, and diverge junctions, where thecells have linear demand functions and affine supply functions with identicalslopes, and the cost is the total traffic volume, we show, using the maximumprinciple, that variable speed limits are not needed in order to achieveoptimality in the FNC problem, and ramp metering is sufficient. We also provebounds on perturbation of the controlled system trajectory in terms ofperturbations in initial traffic volume and exogenous inflows. These bounds,which leverage monotonicity properties of the controlled trajectory, are shownto be in close agreement with numerical simulation results.

Convexity and Robustness of Dynamic Traffic Assignment and Freeway Network Control