Обобщенная лемма Гиббса и равновесие по Вардропу

В.Н. Малоземов, Н.А. Соловьева

Research output

Abstract

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.
Translated title of the contributionA generalized Gibbs’ lemma and a Wardrop equilibrium
Original languageRussian
Pages (from-to)199-211
Number of pages12
Journal ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ
Volume15
Issue number2
DOIs
Publication statusPublished - 2019

Scopus subject areas

  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics
  • Computer Science(all)

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