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**1 - 6**of**6**### -NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of Kobe University ScienceDirect 21st International Symposium on Transportation and Traffic Theory Data-driven linear decision rule approach

, 2015

"... Abstract We propose a two-stage, on-line signal control strategy for dynamic networks using a linear decision rule (LDR) approach and a distributionally robust optimization (DRO) technique. The first (off-line) stage formulates a LDR that maps real-time traffic data to optimal signal control polici ..."

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Abstract We propose a two-stage, on-line signal control strategy for dynamic networks using a linear decision rule (LDR) approach and a distributionally robust optimization (DRO) technique. The first (off-line) stage formulates a LDR that maps real-time traffic data to optimal signal control policies. A DRO problem is then solved to optimize the on-line performance of the LDR in the presence of uncertainties associated with the observed traffic states and ambiguity in their underlying distribution functions. We employ a datadriven calibration of the uncertainty set, which takes into account historical traffic data. The second (on-line) stage implements a very efficient linear decision rule whose performance is guaranteed by the off-line computation. We test the proposed signal control procedure in a simulation environment that is informed by actual traffic data obtained in Glasgow, and demonstrate its full potential in on-line operation and deployability on realistic networks, as well as its effectiveness in improving traffic.

### unknown title

, 2014

"... A junction condition by specified homogenization and application to traffic lights ..."

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A junction condition by specified homogenization and application to traffic lights

### A junction condition by specified homogenization

, 2014

"... Given a coercive Hamiltonian which is quasi-convex with respect to the gradi-ent variable and periodic with respect to time and space at least “far away from the origin”, we consider the solution of the Cauchy problem of the corresponding Hamilton-Jacobi equation posed on the real line. Compact pert ..."

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Given a coercive Hamiltonian which is quasi-convex with respect to the gradi-ent variable and periodic with respect to time and space at least “far away from the origin”, we consider the solution of the Cauchy problem of the corresponding Hamilton-Jacobi equation posed on the real line. Compact perturbations of coercive periodic quasi-convex Hamiltonians enter into this framework for example. We prove that the rescaled solution converges towards the solution of the expected effective Hamilton-Jacobi equation, but whose “flux ” at the origin is limited in the sense of (Imbert, Monneau [9]). In other words, the homogenization of such a Hamilton-Jacobi equation yields to supplement the expected homogenized Hamilton-Jacobi equation with a junction condition at the single discontinuous point of the effective Hamiltonian. We also illustrate possible applications of such a result by deriving, for a traffic flow problem, the effective flux limiter generated by the presence of a finite number of traffic lights on an ideal road. AMS Classification: 35F21, 49L25, 35B27

### A junction condition by specified homogenization

, 2014

"... Given a coercive Hamiltonian which is quasi-convex with respect to the gradi-ent variable and periodic with respect to time and space at least “far away from the origin”, we consider the solution of the Cauchy problem of the corresponding Hamilton-Jacobi equation posed on the real line. Compact pert ..."

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Given a coercive Hamiltonian which is quasi-convex with respect to the gradi-ent variable and periodic with respect to time and space at least “far away from the origin”, we consider the solution of the Cauchy problem of the corresponding Hamilton-Jacobi equation posed on the real line. Compact perturbations of coercive periodic quasi-convex Hamiltonians enter into this framework for example. We prove that the rescaled solution converges towards the solution of the expected effective Hamilton-Jacobi equation, but whose “flux ” at the origin is limited in the sense of (Imbert, Monneau [9]). In other words, the homogenization of such a Hamilton-Jacobi equation yields to supplement the expected homogenized Hamilton-Jacobi equation with a junction condition at the single discontinuous point of the effective Hamiltonian. We also illustrate possible applications of such a result by deriving, for a traffic flow problem, the effective flux limiter generated by the presence of a finite number of traffic lights on an ideal road.