arXiv subjects

Marius Schmitt

Publications and source records attributed to Marius Schmitt.

6 recordsLinked to original sources

arXiv2018

An Exact Convex Relaxation of the Freeway Network Control Problem with Controlled Merging Junctions

We consider the freeway network control problem where the aim is to optimize the operation of traffic networks modeled by the Cell Transmission Model via ramp metering and partial mainline demand control. Optimal control problems using the Cell Transmission Model are usually non-convex, due to the nonlinear fundamental diagram, but a convex relaxation in which demand and supply constraints are relaxed is often used. Previous works have established conditions under which solutions of the relaxation can be made feasible with respect to the original constraints. In this work, we generalize these conditions and show that the control of flows into merging junctions is sufficient to do so if the objective is to minimize the total time spent in traffic. We derive this result by introducing an alternative system representation. In the new representation, the system dynamics are concave and state-monotone. We show that exactness of the convex relaxation of finite horizon optimal control problems follows from these properties. Deriving the main result via a characterization of the system dynamics allows one to treat arbitrary monotone, concave fundamental diagrams and several types of control for merging junctions in a uniform manner. The derivation also suggests a straightforward method to verify if the results continue to hold for extensions or modifications of the models studied in this work.

math.OC↗

arXiv2018

On monotonicity of FIFO-diverging junctions

This technical note concerns the dynamics of FIFO-diverging junctions in compartmental models for traffic networks. Many strong results on the dynamical behavior of such traffic networks rely on monotonicity of the underlying dynamics. In road traffic modeling, a common model for diverging junctions is based on the First-in, first-out principle. These type of junctions pose a problem in the analysis of traffic dynamics, since their dynamics are not monotone with respect to the positive orthant. However, this technical note demonstrates that they are in fact monotone with respect to the partial order induced by a particular, polyhedral cone.

math.DS↗

arXiv2018

A Convex Reformulation of the Robust Freeway Network Control Problem with Controlled Merging Junctions

In the freeway network control (FNC) problem, the operation of a traffic network is optimized using only flow control. For special cases of the FNC problem, in particular the case when all merging flows are controlled, there exist tight convex relaxations of the corresponding optimization problem. However, model uncertainty, in particular regarding the fundamental diagram and predictions of future traffic demand, can be a problem in practice. This uncertainty poses a challenge to control approaches that pursue a model- and optimization-based strategy. In this work, we propose a robust counterpart to the FNC problem, where we introduce uncertainty sets for both the fundamental diagram and future, external traffic demands and seek to optimize the system operation, minimizing the worst-case cost. For a network with controlled merging junctions, and assuming that certain technical conditions on the uncertainty sets are satisfied, we show that the robust counterpart of the FNC problem can be reduced to a convex, finite-dimensional and deterministic optimization problem, whose numerical solution is tractable.

math.OC↗

arXiv2017

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

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.

math.OC↗

arXiv2017

An Integrated and Scalable Platform for Proactive Event-Driven Traffic Management

Traffic on freeways can be managed by means of ramp meters from Road Traffic Control rooms. Human operators cannot efficiently manage a network of ramp meters. To support them, we present an intelligent platform for traffic management which includes a new ramp metering coordination scheme in the decision making module, an efficient dashboard for interacting with human operators, machine learning tools for learning event definitions and Complex Event Processing tools able to deal with uncertainties inherent to the traffic use case. Unlike the usual approach, the devised event-driven platform is able to predict a congestion up to 4 minutes before it really happens. Proactive decision making can then be established leading to significant improvement of traffic conditions.

cs.AI↗

arXiv2016

Distributed Learning in the Presence of Disturbances

We consider a problem where multiple agents must learn an action profile that maximises the sum of their utilities in a distributed manner. The agents are assumed to have no knowledge of either the utility functions or the actions and payoffs of other agents. These assumptions arise when modelling the interactions in a complex system and communicating between various components of the system are both difficult. In [1], a distributed algorithm was proposed, which learnt Pareto-efficient solutions in this problem setting. However, the approach assumes that all agents can choose their actions, which precludes disturbances. In this paper, we show that a modified version of this distributed learning algorithm can learn Pareto-efficient solutions, even in the presence of disturbances from a finite set. We apply our approach to the problem of ramp coordination in traffic control for different demand profiles.

eess.SY↗