Deep Learning Method for Stationary Distribution of RBM

Reflected Brownian motion (RBM) plays an important role in the analysis of multiclass queueing networks, where it often arises as a di!usion approximation under heavy tra''c. In such settings, the stationary distribution of an RBM provides useful approximations for the steady-state behavior of the underlying queueing network. Closed-form expressions for stationary distributions are known only for a few special classes of RBMs. This paper develops a scalable deep learning method for computing the Laplace transform of the stationary distribution of a high dimensional RBM. The computed Laplace transforms can be used to estimate tail probabilities that serve as important performance metrics, such as latency for queueing networks.