Distributed resource management using iterative gradient update synthesis

We consider load balancing on a network. Servers of limited bandwidth move a single commodity through a network of buffers (or queues) while external random processes generate and consume this commodity. Our contribution is a distributed algorithm for regulating the backlogs of these queues to a given reference while balancing the mean flow in the network. We formulate this as a fluid buffer regulation problem and use distributed gradient descent to update the feedback gains for an LQG controller. Our proposed distributed algorithm both implicitly and explicitly estimates the statistics of the external process flows using only local information on fixed time intervals and updates the feedback matrix for the regulator accordingly. We demonstrate our method on a simulation of an industrial floor where autonomous vehicles remove palettes from production line buffers.