Impulsive Control for G-AIMD Dynamics with Relaxed and Hard Constraints

Konstantin Avrachenkov (1) , Alexei Piunovskiy (2) , Yi Zhang (2)

1 NEO - Network Engineering and Operations
2 Department of Mathematical Sciences [Liverpool]

Motivated by various applications from Internet congestion control to power control in smart grids and electric vehicle charging, we study Generalized Additive Increase Multiplicative Decrease (G-AIMD) dynamics under impulsive control in continuous time with the time average alpha-fairness criterion. We first show that the control under relaxed constraints can be described by a threshold. Then, we propose a Whittle-type index heuristic for the hard constraint problem. We prove that in the homogeneous case the index policy is asymptotically optimal when the number of users is large.

Mots clés: Impulsive control problem; Whittle index; Internet congestion control; Power control problems; Electric vehicle charging

Domaines: Optimisation et contrôle [math.OC]; Réseaux et télécommunications [cs.NI]

Konstantin Avrachenkov, Alexei Piunovskiy, Yi Zhang. Impulsive Control for G-AIMD Dynamics with Relaxed and Hard Constraints. IEEE CDC 2018, Dec 2018, Miami Beach, United States. ⟨hal-01966182⟩