  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.
