Best Effort Workload Disparity Minimization in Multi-Agent Systems with Capacity Constraints

In this paper we propose a load balancing problem formulation where agents cooperate with the aim of simultaneously minimizing both the workload disparity among the agents and the overall workload transfer, under network capacity constraints. Notably, in our computational setting, the network is not just a device for the distributed solution of an optimization problem; on the contrary, the problem shares the same sparsity pattern as the network, and this aspect allows to solve it without the need for the agents to store large amount of data. In particular, while the load balancing process occurs over directed links, agents' communication is assumed to be bidirectional. For this optimization setting, first, an optimality condition is derived; then, a provably convergent distributed algorithm to compute the optimal solution is developed, and an upper bound on the convergence rate is characterized. Simulation results are provided to corroborate the validity and performance of our theoretical findings.