  The most widely applied strategy for workload sharing is to equalize the
workload assigned to each resource. In mobile multi-agent systems, this
principle directly leads to equitable partitioning policies in which (i) the
workspace is divided into subregions of equal measure, (ii) there is a
bijective correspondence between agents and subregions, and (iii) each agent is
responsible for service requests originating within its own subregion. In this
paper, we design provably correct, spatially-distributed and adaptive policies
that allow a team of agents to achieve a convex and equitable partition of a
convex workspace, where each subregion has the same measure. We also consider
the issue of achieving convex and equitable partitions where subregions have
shapes similar to those of regular polygons. Our approach is related to the
classic Lloyd algorithm, and exploits the unique features of power diagrams. We
discuss possible applications to routing of vehicles in stochastic and dynamic
environments. Simulation results are presented and discussed.
