Develops implementable scheduling, routing, and admission-control policies for stochastic processing networks based on numerical solutions of Brownian control problems.

Establishes functional limits for generalized Jackson networks in multiscale heavy traffic, characterizing asymptotic independence across scales and the dependence of limiting dynamics on initial conditions.

Establishes a product-form limit with independent exponential components for scaled SRBM steady-state distributions in a multiscaling regime, verifying the required moment bounds for several classes of reflection matrices.

Establishes uniform moment bounds for scaled steady-state queue lengths in generalized Jackson networks under multiscale heavy traffic, verifying the moment state-space-collapse condition needed for product-form stationary limits.

Develops a framework for evaluating datacenter congestion-control algorithms using confidence intervals and trial-count prediction, with importance sampling to improve the efficiency of tail-quantile estimation.

Establishes heavy-traffic steady-state limits for join-the-shortest-queue and power-of-two-choices routing with general interarrival and service-time distributions, proving convergence of scaled queue lengths to a common exponential limit.

Develops a regenerative simulation algorithm with importance sampling to estimate tail quantiles of steady-state sojourn times in non-preemptive priority queues, with a central limit theorem supporting confidence intervals.

Develops and validates a queueing-network simulation model for hospital ultrasound operations, with two-level patient routing calibrated using machine learning to improve predictions of queue lengths and waiting-time distributions.