Optimal scenario for road evacuation in an urban environment

How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem. We consider a macroscopic road traffic model on networks, se...

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Vydáno v:Zeitschrift für angewandte Mathematik und Physik
Hlavní autoři: Bestard, Mickael, Franck, Emmanuel, Navoret, Laurent, Privat, Yannick
Médium: Journal Article
Jazyk:angličtina
Vydáno: Springer Verlag 2024
Témata:
Analysis of PDEs
Mathematics
Numerical Analysis
Optimization and Control
Hyperbolic PDE
Optimal Control
Optimization methods
Fluid model
Traffic network
ISSN:0044-2275, 1420-9039
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Shrnutí:How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem. We consider a macroscopic road traffic model on networks, semi-discretized in space and decide to give ourselves the possibility to control the flow at junctions. Our target is to smooth the traffic along a given path within a fixed time. A parsimony constraint is imposed on the controls, in order to ensure that the optimal strategies are feasible in practice.We perform an analysis of the resulting optimal control problem, proving the existence of an optimal control and deriving optimality conditions, which we rewrite as a single functional equation. We then use this formulation to derive a new mixed algorithm interpreting it as a mix between two methods: a descent method combined with a fixed point method allowing global perturbations. We verify with numerical experiments the efficiency of this method on examples of graphs, first simple, then more complex. We highlight the efficiency of our approach by comparing it to standard methods. We propose an open source code implementing this approach in the Julia language.
ISSN:0044-2275
1420-9039
DOI:10.48550/arXiv.2310.15359