**Date & Time:** Tuesday, August 11, 2015, 15:30-16:30

**Venue:** Ramanujan Hall

**Title:** Construction of Asymptotically Optimal Control for a Stochastic
Network from a Free Boundary Problem

**Speaker:** Subhamay Saha, Technion

**Abstract:** An asymptotic framework for optimal control of multiclass
stochastic processing networks, using formal diffusion approximations
under suitable temporal and spatial scaling, by Brownian control problems
(BCP) and their equivalent workload formulations (EWF), has been developed
by Harrison (1988). This framework has been implemented in many works for
constructing asymptotically optimal control policies for a broad range of
stochastic network models.To date all asymptotic optimality results for
such networks correspond to settings where the solution of the EWF is a
reflected Brownian motion in the positive orthant with normal
reflections.In this work we consider a well studied stochastic network
which is perhaps the simplest example of a model with more than one
dimensional workload process. In the regime considered here, the singular
control problem corresponding to the EWF does not have a simple form
explicit solution, however by considering an associated free boundary
problem one can give a representation for an optimal controlled process as
a two dimensional reflected Brownian motion in a Lipschitz domain whose
boundary is determined by the solution of the free boundary problem. Using
the form of the optimal solution we propose a sequence of control
policies, given in terms of suitable thresholds, for the scaled stochastic
network control problems and prove that this sequence of policies is
asymptotically optimal. As suggested by the solution of the EWF, the
policy we propose requires a server to idle under certain conditions which
are specified in terms of the thresholds determined from the free
boundary.
This is a joint work with A. Budhiraja and X. Liu.