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Sufficient Optimality Conditions for Distributed, Non-Predictive Ramp Metering in the Monotonic Cell Transmission Model


M. Schmitt, C. Ramesh, J. Lygeros

Submitted to Journal of Transportation Research Part B: Methodological

We consider the freeway ramp metering problem, based on the Cell Transmission Model. Assuming perfect model knowledge and perfect traffic demand prediction, the ramp metering problem can be cast as a finite horizon optimal control problem with the objective of minimizing the Total Time Spent, i.e., the sum of the travel times of all drivers. For this reason, the application of Model Predictive Control (MPC) to the ramp metering problem has been proposed. However, practical tests on freeways show that MPC rarely outperforms simple, decentralized feedback strategies. Until now, a theoretical justification for this empirical observation is lacking. This work compares the performance of distributed, non- predictive feedback strategies to the optimal solution. To do so, we propose a distributed, non-predictive controller, and show that this controller preserves monotonicity of the closed-loop system. We exploit this result to derive sufficient conditions under which the distributed controller achieves globally optimal performance. In a small case study based on real-world traffic data, we also demonstrate that these optimality conditions are rarely violated on a typical day. In addition, even in cases when they are violated, the performance deterioration is shown to be negligibly small.


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% Autogenerated BibTeX entry
@Article { SchRam:2016:IFA_5531,
    author={M. Schmitt and C. Ramesh and J. Lygeros},
    title={{Sufficient Optimality Conditions for Distributed,
	  Non-Predictive Ramp Metering in the Monotonic Cell
	  Transmission Model}},
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