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Dynamic route choice as an aggregative game

Author(s):

G. Burger
Conference/Journal:

Semester Thesis, FS16 (10528)
Abstract:

In this semester project we studied a road network. Our goal was to find a way to compute how different users would interact on this network. We consider that each user wants to send a certain number of cars on the network and are interacting noncooperatively on the network. Each user aims at minimizing the total travel time and at arriving at a specific time. We got interested in this topics because on literature, most of the results that exist and are broadly used nowadays are about static models. There already exist several dynamics model and algorithm to solve this problem. But until now, very few theoretical guarantees have been given about dynamics model. We therefore wanted to get some insight in the topics and see where the dfficulties laid. In an attempt to solve this problem, we first came up with a dynamics model to describe how cars will travel on the network. We used this model to describe the interaction of the users as a game. From this game, we tried to compute an equilibrium. Indeed the equilibrium of this game represents a possible interaction between the different players trying selfishly to fulfill their objectives. For this purpose we used the Variational Inequality which is a useful tool when computing such a kind of minimisation. Once we had expressed the basis of our model, we looked at a numerical algorithm that could find the desired equilibrium. This algorithm needed some properties from our model to converge. We studied those and proved for a reduced case that our algorithm would converge for sure. While studying the converging properties, we found that, in specific cases, the equilibrium of the game could be computed. This result is interesting and even better than the numerical convergence, however, it is applicable for a much more restricted range of games.

Supervisors: Basilio Gentile, Dario Paccagnan, John Lygeros

Year:

2016
Type of Publication:

(13)Semester/Bachelor Thesis
Supervisor:



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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2016:IFA_5459
}
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