Resource Sharing Networks and Brownian Control Problems

Abstract

We consider a family of resource sharing networks that were introduced in the work of Massoulié and Roberts (2000) as models for Internet flows and study an optimal stochastic control problem associated with the dynamic allocation of resource capacities to jobs in the system. Since these stochastic control problems are in general intractable, we analyze the system in a heavy traffic regime where one can formally approximate these control problems by certain Brownian control problems (BCP). It is shown that, both for a discounted cost and an ergodic cost criterion, an appropriate BCP gives a lower bound on the best achievable asymptotic cost under any sequence of admissible policies. The lower bounds established in this work show that the threshold control policies constructed in Budhiraja and Johnson (2017), which achieve the Hierarchical Greedy Ideal (HGI) performance (cf. Harrison et al. (2014)) in the heavy traffic limit, are in fact asymptotically optimal when certain monotonicity conditions on the cost function are satisfied.