Approximate Bayesian inference with queueing networks and coupled jump processes
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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.
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