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Instantaneous control for traffic flow. (English) Zbl 1117.90030
Summary: The solution methods for optimal control problems with coupled partial differential equations as constraints are computationally costly and memory intensive; in particular for problems stated on networks, this prevents the methods from being relevant. We present instantaneous control problems for the optimization of traffic flow problems on road networks. We derive the optimality conditions, investigate the relation to the full optimal control problem and prove that certain properties of the optimal control problem carry over to the instantaneous one. We propose a solution algorithm and compare quality of the computed controls and run-times.

MSC:
90B20 Traffic problems in operations research
35L99 Hyperbolic equations and hyperbolic systems
90B10 Deterministic network models in operations research
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