Traffic Assignment & Gibbs-Maslov Semirings

LOTITO P.A; MANCINELLI, E.M.; QUADRAT, J.-P.

Contemporary Mathematics

American Mathematical Society

Lugar: Providence, Rhode Island, USA; Año: 2005; p. 209 - 220

Abstract: The Trafficc Assignment problem consists in determining the routes used by sets of network users taking into account the link congestions. In deterministic modelling, Wardrop Equilibriums are computed. They can be reduced to huge non-linear multiow problems in the simplest cases. In stochastic modelling, Logit Assignments are used. They are obtained, mainly, by substituting the minplus semiring by the Gibbs-Maslov semirings" x+y =max(x,y) in the deterministic assignment computations. Key-words: semiring, trac assignment, Wardrop equilibrium, maxplus algebra, quantization, logit semiring, trac assignment, Wardrop equilibrium, maxplus algebra, quantization, logit Key-words: semiring, trac assignment, Wardrop equilibrium, maxplus algebra, quantization, logit semiring, trac assignment, Wardrop equilibrium, maxplus algebra, quantization, logit The Trafficc Assignment problem consists in determining the routes used by sets of network users taking into account the link congestions. In deterministic modelling, Wardrop Equilibriums are computed. They can be reduced to huge non-linear multiow problems in the simplest cases. In stochastic modelling, Logit Assignments are used. They are obtained, mainly, by substituting the minplus semiring by the Gibbs-Maslov semirings" x+y =max(x,y) in the deterministic assignment computations. Key-words: semiring, trac assignment, Wardrop equilibrium, maxplus algebra, quantization, logit semiring, trac assignment, Wardrop equilibrium, maxplus algebra, quantization, logit