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 .
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 .
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give rise to complex families of stochastic processes, and
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Yet, despite their importance within applications, and in comparison to their counterpart stochastic
In comparison to counterpart
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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
the stochastic (jump)
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. 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
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