Advection on networks with an application to decentralized load balancing

This paper examines an advection-based protocol for the coordination of a networked, multi-agent system. Diffusion forms the basis of the popular consensus dynamics and is closely related to advection. It is with this motivation that we examine a discretized version of advection over a network with the flow field realized through directed graph edges. We endeavor to demonstrate that the subsequent advection protocol forms an attractive set of system dynamics for coordinated control. This paper includes a formulation of the advection dynamics on directed graphs and a presentation of some of its characteristics. We also demonstrate the versatility of the advection dynamics with a decentralized load balancing application.