PreprintCC BY 4.0HAL
Green waves III: Best and worst offsets for a line of traffic lights (Preliminary version)
Abstract
We consider an infinite road with equally spaced traffic lights. The lights have a common period and a fixed offset between consecutive lights. For a triangular flux, we study the effective flux obtained by homogenization of a Hamilton-Jacobi equation. Using an explicit formula, we find conditions under which forward and backward green waves maximize the flow in fluid and congested traffic, respectively. When the two green-wave offsets give the same signals, a single offset is optimal at every density. We also estimate the loss of flow for any offset. This loss tends to zero as the distance between the lights increases. The estimate is sharp and is attained by red waves in light or heavy traffic.
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BibTeX
@misc{assi2026green,
title = {{Green waves III: Best and worst offsets for a line 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-05837529v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Green waves III: Best and worst offsets for a line 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-05837529v1
AB - We consider an infinite road with equally spaced traffic lights. The lights have a common period and a fixed offset between consecutive lights. For a triangular flux, we study the effective flux obtained by homogenization of a Hamilton-Jacobi equation. Using an explicit formula, we find conditions under which forward and backward green waves maximize the flow in fluid and congested traffic, respectively. When the two green-wave offsets give the same signals, a single offset is optimal at every density. We also estimate the loss of flow for any offset. This loss tends to zero as the distance between the lights increases. The estimate is sharp and is attained by red waves in light or heavy traffic.
ER -