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Abstract: We study the distribution of traffic in networks whose users try to minimisetheir delays by adhering to a simple learning scheme inspired by the replicatordynamics of evolutionary game theory. The stable steady states of thesedynamics coincide with the network-s Wardrop equilibria and form a convexpolytope whose dimension is determined by the network-s redundancy animportant concept which measures the -linear dependence- of the users- paths.Despite this abundance of stationary points, the long-term behaviour of thereplicator dynamics turns out to be remarkably simple: every solution orbitconverges to a Wardrop equilibrium.On the other hand, a major challenge occurs when the users- delays fluctuateunpredictably due to random external factors. In that case, interior equilibriaare no longer stationary, but strict equilibria remain stochastically stableirrespective of the fluctuations- magnitude. In fact, if the network has noredundancy and the users are patient enough, we show that the long-termaverages of the users- traffic flows converge to the vicinity of anequilibrium, and we also estimate the corresponding invariant measure.



Autor: Panayotis Mertikopoulos, Aris L. Moustakas

Fuente: https://arxiv.org/







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