Differentiated consensuses in decentralized load balancing problem with randomized topology, noise, and delays

In this paper, a new consensus problem, termed differentiated consensuses, is studied. This consensus problem is that, in a system with multiple classes, consensus is targeted for each class, which may be different among classes. Specifically, we investigate differentiated consensuses in a distributed stochastic network system of nodes (or agents), where tasks, classified with different priorities, are serviced. The network system is assumed to have switched topology, noise and delay in measurement, and cost on the topology. The goal is to reach/maintain balanced (equal) load, i.e. consensus, across the network and at the same time to meet the topology cost constraint, both for every priority class. A control protocol is proposed. We prove that the proposed control protocol is able to meet the topology cost constraint and achieve approximate consensus for each of the priority classes in the network.