7 research outputs found
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,
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
State elimination for mixed-integer optimal control of partial differential equations by semigroup theory
Mixed-integer optimal control problems governed by partial differential equations (MIPDECOs) are powerful modeling tools but also challenging in terms of theory and computation. We propose a highly efficient state elimination approach for MIPDECOs that are governed by partial differential equations that have the structure of an abstract ordinary differential equation in function
space. This allows us to avoid repeated calculations of the states for all time steps, and our approach is applied only once before starting the optimization. The presentation of theoretical results is complemented by numerical experiments
On the optimization of conservation law models at a junction with inflow and flow distribution controls
The paper proposes a general framework to analyze control problems for
conservation law models on a network. Namely we consider a general class of
junction distribution controls and inflow controls and we establish the
compactness in of a class of flux-traces of solutions. We then derive the
existence of solutions for two optimization problems: (I) the maximization of
an integral functional depending on the flux-traces of solutions evaluated at
points of the incoming and outgoing edges; (II) the minimization of the total
variation of the optimal solutions of problem (I). Finally we provide an
equivalent variational formulation of the min-max problem (II) and we discuss
some numerical simulations for a junction with two incoming and two outgoing
edges.Comment: 29 pages, 14 figure
Transit-Based Emergency Evacuation with Transit Signal Priority in Sudden-Onset Disaster
This study presents methods of transit signal priority without transit-only lanes for a transit-based emergency evacuation in a sudden-onset disaster. Arterial priority signal coordination is optimized when a traffic signal control system provides priority signals for transit vehicles along an evacuation route. Transit signal priority is determined by “transit vehicle arrival time estimation,” “queuing vehicle dissipation time estimation,” “traffic signal status estimation,” “transit signal optimization,” and “arterial traffic signal coordination for transit vehicle in evacuation route.” It takes advantage of the large capacities of transit vehicles, reduces the evacuation time, and evacuates as many evacuees as possible. The proposed methods were tested on a simulation platform with Paramics V6.0. To evaluate and compare the performance of transit signal priority, three scenarios were simulated in the simulator. The results indicate that the methods of this study can reduce the travel times of transit vehicles along an evacuation route by 13% and 10%, improve the standard deviation of travel time by 16% and 46%, and decrease the average person delay at a signalized intersection by 22% and 17% when the traffic flow saturation along an evacuation route is 0.8<V/C≤1.0 and V/C>1.0, respectively
Multiscale methods for traffic flow on networks
In this thesis we propose a model to describe traffic
flows on network by the theory of measure-based
equations. We first apply our approach to the initial/boundary-value problem for the measure-valued
linear transport equation on a bounded interval, which is the prototype of an arc of the network.
This simple case is the first step to build the solution of the respective linear problem on networks:
we construct the global solution by gluing all the measure-valued solutions on the arcs by means of
appropriate distribution rules at the vertices.
The linear case is adopted to show the well-posedness for the transport equation on networks in case of
nonlocal velocity fields, i.e. which depends not only on the state variable, but also on the solution itself.
It is also studied a representation formula in terms of the push-forward of the initial and boundary
data along the network along the admissible trajectories, weighted by a properly dened measure on
curves space. Moreover, we discuss an example of nonlocal velocity eld tting our framework and
show the related model features with numerical simulations.
In the last part, we focus on a class of optimal control problems for measure-valued nonlinear transport
equations describing traffic
ow problems on networks. The objective is to optimize macroscopic
quantities, such as traffic volume, average speed, pollution or average time in a fixed area, by controlling
only few agents, for example smart traffic lights or automated cars. The measure-based approach
allows to study in the same setting local and nonlocal drivers interactions and to consider the control
variables as additional measures interacting with the drivers distribution. To complete our analysis,
we propose a gradient descent adjoint-based optimization method and some numerical experiments in
the case of smart traffic lights for a 2-1 junction