Controlling G-AIMD by index policy

We consider the Generalized Additive Increase Multiplicative Decrease (G-AIMD) dynamics for resource allocation with alpha fairness utility function. This dynamics has a number of important applications such as internet congestion control, charging electric vehicles, and smart grids. We prove indexability for the special case of MIMD model and provide an efficient scheme to compute the index. The use of index policy allows us to avoid the curse of dimensionality. We also demonstrate through simulations for another special case, AIMD, that the index policy is close to optimal and significantly outperforms a natural heuristic which penalizes the strongest user.