Control Policies Approaching Hierarchical Greedy Ideal Performance in Heavy Traffic for Resource Sharing Networks

We consider resource sharing networks of the form introduced in work of Massoulié and Roberts as models for Internet flows. The goal is to study the open problem, formulated in Harrison et al. (2014) [Harrison JM, Mandayam C, Shah D, Yang Y (2014) Resource sharing networks: Overview and an open problem. Stochastic Systems 4(2):524–555.], of constructing simple form rate-allocation policies for broad families of resource sharing networks with associated costs converging to the hierarchical greedy ideal performance in the heavy traffic limit. We consider two types of cost criteria: an infinite horizon discounted cost and a long-time average cost per unit time. We introduce a sequence of rate-allocation control policies that are determined in terms of certain thresholds for the scaled queue-length processes and prove that, under conditions, both type of costs associated with these policies converge in the heavy traffic limit to the corresponding hierarchical greedy ideal (HGI) performance. The conditions needed for these results are satisfied by all the examples considered in the above cited paper of Harrison et al.