Variational inequalities and mean-field approximations for partially observed systems of queueing networks

TL;DR

This paper introduces a novel variational framework for partially observed queueing networks, enabling efficient mean-field approximations and improved inference in complex interconnected systems.

Contribution

It presents a model augmentation and variational approach that handle partial observations and complex interactions, advancing analysis of queueing networks.

Findings

Enables variational evaluation of mean-field measures for partially observed networks.

Provides an efficient alternative for inference tasks in complex queueing systems.

Improves upon existing variational and numerical methods for these models.

Abstract

Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump) processes induced by queueing networks have distinctive coupling and synchronization properties. This has prevented the derivation of variational approximations for conditional representations of transient dynamics, which rely on simplifying independence assumptions. Here, we present a model augmentation to a multivariate counting process for interactions across service stations, and we enable the variational evaluation of mean-field measures for partially-observed multi-class networks. We also show that our framework offers an efficient and improved alternative for inference tasks, where existing variational or numerically intensive solutions do not work.