Title: Approximate Bayesian inference with queueing networks and coupled jump processes,
Abstract: Queueing networks are systems of theoretical interest that give rise to
complex families of stochastic processes, and find widespread use in the
performance evaluation of interconnected resources. Yet, despite their
importance within applications, and in comparison to their counterpart
stochastic models in genetics or mathematical biology, there exist few relevant
approaches for transient inference and uncertainty quantification tasks in
these systems. This is a consequence of strong computational impediments and
distinctive properties of the Markov jump processes induced by queueing
networks. In this paper, we offer a comprehensive overview of the inferential
challenge and its comparison to analogue tasks within related mathematical
domains. We then discuss a model augmentation over an approximating network
system, and present a flexible and scalable variational Bayesian framework,
which is targeted at general-form open and closed queueing systems, with varied
service disciplines and priorities. The inferential procedure is finally
validated in a couple of uncertainty quantification tasks for network service
rates.