PreprintCC BY 4.0HAL
Green Waves II: a variational approach to homogenization of lines of traffic lights (preliminary version)
Abstract
We consider a infinite line of traffic lights, with equidistance 1, and 1-periodic in time. They are red during a period of time equal to θ ∈ [0, 1] and green during a period of time 1 -θ. The offset between two consecutive traffic lights is fixed to φ ∈ R. Given a convex Hamiltonian H, we compute by homogenization the effective Hamiltonian H associated to the infinite line of traffic lights. Using optimal control arguments, we get an explicit formula for the effective Hamiltonian. Our approach is geometric and is based on calculus of variations.
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BibTeX
@misc{assi2026green,
title = {{Green Waves II: a variational approach to homogenization of lines of traffic lights (preliminary version)}},
author = {Ali Assi and Nicolas Forcadel and Regis Monneau},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05837656v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Green Waves II: a variational approach to homogenization of lines of traffic lights (preliminary version)
AU - Ali Assi
AU - Nicolas Forcadel
AU - Regis Monneau
PY - 2026
DA - 2026/10/23
PB - HAL
UR - https://hal.science/hal-05837656v1
AB - We consider a infinite line of traffic lights, with equidistance 1, and 1-periodic in time. They are red during a period of time equal to θ ∈ [0, 1] and green during a period of time 1 -θ. The offset between two consecutive traffic lights is fixed to φ ∈ R. Given a convex Hamiltonian H, we compute by homogenization the effective Hamiltonian H associated to the infinite line of traffic lights. Using optimal control arguments, we get an explicit formula for the effective Hamiltonian. Our approach is geometric and is based on calculus of variations.
ER -