The Convergence of Finite-Averaging of AIMD for Distributed Heterogeneous Resource Allocations

In several social choice problems, agents collectively make decisions over the allocation of multiple divisible and heterogeneous resources with capacity constraints to maximize utilitarian social welfare. The agents are constrained through computational or communication resources or privacy considerations. In this paper, we analyze the convergence of a recently proposed distributed solution that allocates such resources to agents with minimal communication. It is based on the randomized additive-increase and multiplicative-decrease (AIMD) algorithm. The agents are not required to exchange information with each other, but little with a central agent that keeps track of the aggregate resource allocated at a time. We formulate the time-averaged allocations over finite window size and model the system as a Markov chain with place-dependent probabilities. Furthermore, we show that the time-averaged allocations vector converges to a unique invariant measure, and also, the ergodic property holds.