Current distributed routing control algorithms for dynamic networks model networks using the time evolution of density at network edges, while the routing control algorithm ensures edge density to converge to a Wardrop equilibrium, which was characterized by an equal traffic density on all used paths. We rearrange the density model to recast the problem within the framework of mean-field games. In doing that, we illustrate an extended state-space solution approach and we study the stochastic case where the density evolution is driven by a Brownian motion. Further, we investigate the case where the density evolution is perturbed by a bounded adversarial disturbance. For both the stochastic and the worst-case scenarios, we provide conditions for the density to converge to a pre-assigned set. Moreover, we analyze such conditions from two different perspectives, repeated games with vector payoffs and inclusion theory.

Bauso, D., Zhang, X., Papachristodoulou, A. (2016). Density Flow in Dynamical Networks via Mean-Field Games. IEEE TRANSACTIONS ON AUTOMATIC CONTROL [10.1109/TAC.2016.2584979].

Density Flow in Dynamical Networks via Mean-Field Games

D. Bauso
;
2016-01-01

Abstract

Current distributed routing control algorithms for dynamic networks model networks using the time evolution of density at network edges, while the routing control algorithm ensures edge density to converge to a Wardrop equilibrium, which was characterized by an equal traffic density on all used paths. We rearrange the density model to recast the problem within the framework of mean-field games. In doing that, we illustrate an extended state-space solution approach and we study the stochastic case where the density evolution is driven by a Brownian motion. Further, we investigate the case where the density evolution is perturbed by a bounded adversarial disturbance. For both the stochastic and the worst-case scenarios, we provide conditions for the density to converge to a pre-assigned set. Moreover, we analyze such conditions from two different perspectives, repeated games with vector payoffs and inclusion theory.
2016
Settore MAT/09 - Ricerca Operativa
Settore ING-INF/04 - Automatica
Bauso, D., Zhang, X., Papachristodoulou, A. (2016). Density Flow in Dynamical Networks via Mean-Field Games. IEEE TRANSACTIONS ON AUTOMATIC CONTROL [10.1109/TAC.2016.2584979].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/253189
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