Before revision:  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 .
After revision:  This is a consequence of strong computational impediments and distinctive properties of the Markov 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 .