Abstract
Designing optimal incentive mechanisms for electric vehicles is an important challenge nowadays. In fact, this new type of vehicle influences several parts of society, at the transport level through congestion/pollution and at the energy level. In this paper, we consider the design of driving and charging optimal incentive through a routing game approach with multiple types of vehicles: gasoline and electric. We show that the game is not standard and needs a particular framework. We are able to prove the existence of a Wardrop equilibrium of this routing game with nonseparable costs, due to interaction through the energy cost. Our analysis is applied to a particular transportation network in which two paths are possible for vehicles, mainly one through the city center and another one outside. A fully characterization of Wardrop equilibrium is proposed, and optimal tolls are computed in order to minimize an environmental cost. Numerical results are provided on real data of electricity consumptions in France and in Texas, USA.
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Notes
- 1.
See, e.g., the case of “Ile-de-France,” compared to France where the current number of EV in circulation is around 150 000 http://www.automobile-propre.com/dossiers/voitures-electriques/chiffres-vente-immatriculations-france/ when the total number of French vehicles of around 39 millions.
- 2.
Such incentive mechanism is already applied in practice, in metropolis like London (https://tfl.gov.uk/modes/driving/congestion-charge).
- 3.
Costs functions are separable if \(c(x)=c_a(x_a)\) for all arc a, \(x_a\) being the flow on a.
- 4.
It does not include dynamic or locational effects.
- 5.
For greater details of the proofs, please visit https://sites.google.com/site/olivierbeaudes-homepage/olivier-beaude-publications.
- 6.
Data are available at https://www.enedis.fr/coefficients-des-profils.
- 7.
Data are available at http://www.pecanstreet.org/.
- 8.
ENTD \(=\) Enquête Nationale Transports et Déplacements (in French).
- 9.
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Sohet, B., Beaude, O., Hayel, Y. (2019). Routing Game with Nonseparable Costs for EV Driving and Charging Incentive Design. In: Walrand, J., Zhu, Q., Hayel, Y., Jimenez, T. (eds) Network Games, Control, and Optimization. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-10880-9_14
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