title: A generalized Gibbs’ lemma and a Wardrop equilibrium
metadata.name: dc.contributor.author
metadata.value: Malozemov, Vasiliy N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Solovyeva, Natalia A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-07-17T11:53:16Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-07-17T11:53:16Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Malozemov V. N., Solovyeva N. A. A generalized Gibbs’ lemma and a Wardrop equilibrium. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 2, pp. 199–211.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2019.204
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15954
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the article, a generalized Gibbs’ lemma is stated and proved. A conclusion of this lemma corresponds to a definition of Wardrop equilibrium in transport networks. This allows us to naturally introduce a well known convex programming problem with linear constraints whose solution is a Wardrop equilibrium vector. The complicated definition of the Wardrop equilibrium is analyzed in detail (typical examples are given). The reason of the Braess paradox’ appearance is specified. A large example, that illustrates how the Wardrop equilibrium vector changes when a road with zero driving time is added into the transport network, is also given.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 15; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: generalized Gibbs’ lemma
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Wardrop equilibrium
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Braess paradox
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: convex programming
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A generalized Gibbs’ lemma and a Wardrop equilibrium
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 199-211.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15954/1/199-211.pdf
resources.format: Adobe PDF
resources.size: 402,47 kB