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

TL;DR

This paper investigates impulsive control strategies for G-AIMD dynamics across various applications, proposing threshold-based and index heuristics, with proven asymptotic optimality in large homogeneous systems.

Contribution

It introduces a threshold-based control for relaxed constraints and a Whittle-type index heuristic for hard constraints, demonstrating asymptotic optimality in large homogeneous systems.

Findings

Control under relaxed constraints is characterized by a threshold.

A Whittle-type index heuristic is proposed for hard constraints.

Index policy is asymptotically optimal as the number of users grows large.

Abstract

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.