Local voting protocol in decentralized load balancing problem with switched topology, noise, and delays

In this paper the applicability of the local voting protocol with nonvanishing step-size for decentralized stochastic network load balancing is studied under nonstationary problem formulation. The network system was considered to have a switched topology, and the control strategy uses noisy and delayed measurements. Nonvanishing (for example, constant) step-size allows to achieve the better convergence rate and copes with time-varying loads and productivities of agents (nodes). Conditions for achieving a suboptimal level of loading agents are established, and an estimate of the appropriate level of suboptimality is given depending on the step-size of the control algorithm, the structure of the averaged network and the statistical properties of noise and delays in measurements. Obtained theoretical results are illustrated by simulations of simultaneously processing of 10⁶ tasks by 1024 agents with 2048 links. It is examined that the performance of the adaptive multi-agent strategy with redistribution of tasks among “connected” neighbors is significantly better than the performance of the strategy without redistribution.