  We consider the ramp metering problem for a freeway stretch modeled by 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 may not
outperform simple, distributed feedback policies. Until now, a theoretical
justification for this empirical observation was lacking. This work compares
the performance of distributed, non-predictive policies to the optimal solution
in an idealised setting, specifically, for monotonic traffic dynamics and
assuming perfect model knowledge. To do so, we suggest a distributed,
non-predictive policy and derive sufficient optimality conditions for the
minimization of the Total Time Spent via monotonicity arguments. In a case
study based on real-world traffic data, we demonstrate that these optimality
conditions are only rarely violated. Moreover, we observe that the
suboptimality resulting from such infrequent violations appears to be
negligible. We complement this analysis with simulations in non-ideal settings,
in particular allowing for model mismatch, and argue that Alinea, a successful,
distributed ramp metering policy, comes close to the ideal controller both in
terms of control behavior and in performance.
