Fair and Distributed Dynamic Optimal Transport for Resource Allocation over Networks

Optimal transport is a framework that facilitates the most efficient allocation of a limited amount of resources. However, the most efficient allocation scheme does not necessarily preserve the most fairness. In this paper, we establish a framework which explicitly considers the fairness of dynamic resource allocation over a network with heterogeneous participants. As computing the transport strategy in a centralized fashion requires significant computational resources, it is imperative to develop computationally light algorithm that can be applied to large scale problems. To this end, we develop a fully distributed algorithm for fair and dynamic optimal transport with provable convergence using alternating method of multipliers. In the designed algorithm, each corresponding pair of resource supplier and receiver compute their own solutions and update the transport schemes through negotiation iteratively which do not require a central planner. The distributed algorithm can yield a fair and efficient resource allocation mechanism over a network. We corroborate the obtained results through case studies.