Distributed Low-Effort Load Balancing in the Presence of Time-Delays

In this paper, we investigate the problem of distributed load balancing under network capacity constraints, where the participating agents cooperate with the aim of jointly minimizing both the workload disparity among them as well as the overall workload transfer. Classical approaches for asymptotic convergence to the global optimum in a distributed fashion typically assume timely exchange of information between neighboring agents of a given multi-agent system. This assumption is not necessarily valid in practical settings due to non-commensurate (heterogeneous) communication and processing delays that might affect transmissions at different times. More specifically, we consider what effect multiple heterogeneous time-varying delays, among the agents can have on the distributed load balancing problem. We show that the distributed load balancing problem under bounded heterogeneous time-varying delays is globally asymptotically stable, but the rate of convergence is affected. Bounds on the convergence rate are provided with respect to an upper bound on the delays. Simulation examples are provided to show the validity and performance of our theoretical results.