## Grad Student Seminar: Michael Conroy

**Asymptotic optimality in resource sharing networks **

In this talk we consider a family of resource sharing networks that can model Internet flows when control policies are imposed to allocate resources. A fundamental problem for such systems is to construct optimal policies under admissibility constraints, where optimality is formulated in terms of a cost function. This problem of optimizing for stochastic controls is in general intractable, but in a heavy traffic regime (i.e. when system capacity is approximately balanced with system load), these stochastic control problems can be approximated by so-called Brownian control problems. Essentially what this means is that the state process of the original queue, when rescaled, has a limiting diffusion approximation that is easier to analyze. For both a discounted cost and an ergodic cost criterion, the appropriate diffusion approximation gives a lower bound on the best achievable asymptotic cost under any sequence of admissible policies. Consequently, these bounds show that the particular control policies constructed previously in Budhiraja and Johnson (2015) are in fact asymptotically optimal.