Optimal Capacity Allocation for Sampled Networked Systems

TL;DR

This paper addresses the optimal distribution of limited communication capacity among sensors in networked systems to minimize estimation error, revealing convexity properties and how allocation adapts with capacity changes.

Contribution

It formulates the capacity allocation as a convex optimization problem and analyzes the behavior of optimal sampling rates as total capacity varies.

Findings

Optimal capacity allocation is a unique solution when capacity is large.

Sampling rates increase with total capacity, especially beyond a certain threshold.

The problem is recast as a strictly convex optimization, ensuring a unique optimal solution.

Abstract

We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements. We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above, and that each sample requires the same amount of communication. Our goal is then to find an optimal allocation of the capacity to the sensors so that the average estimation error is minimized. We show that when the total available channel capacity is large, this resource allocation problem can be recast as a strictly convex optimization problem, and hence there exists a unique optimal allocation of the capacity. We further investigate how this optimal allocation varies as the available capacity increases. In particular, we show that if the coupling among the subsystems is weak, then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate, and is strictly increasing if and only if the total sampling rate exceeds a certain threshold.