Thursday, 13:45 - 14:10 h, Room: H 0106


Alexander Gasnikov
Stochastic optimization in the model of correspondences matrix calculation and traffic flow distribution

Coauthor: Evgenia Gasnikova


We considered two problems connecting to each other. The first problem is to interpret a gravitational matrix correspondence model and its proper generalization for Moscow city according to the conception of equilibrium of macro system. We propose an ergodic stochastic Markov dynamic of natural behavior of the residents. At the large values of time this dynamic leads to the stationary distribution measure. And when the number of residents tends to infinity this measure is concentrated in a small vicinity of the most probable macro state. To find this state we have to solve an entropy optimization problem. For this problem we use proper dual barrier-multiplicative stochastic subgradient descent in dual space. The second problems consist in finding traffic flow (stochastic) assignment according to the BMW model and Nesterov-dePalma model. We show that substantially interpreted evolutionary games dynamic in this games theory models can be considered to be the mirror descent subgradient (with prox-function Kullbak-Leibler distance). We also investigate the logit(Gibbs) best responses dynamic (Nash-Vardrop equilibrium isn't assumed unique).


Talk 2 of the contributed session Thu.2.H 0106
"Traffic assignment" [...]
Cluster 13
"Logistics, traffic, and transportation" [...]


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