A Bayesian Approach to Parameter Inference in Queueing Networks

Wang, Weikun; Casale, Giuliano; Sutton, Charles

doi:10.1145/2893480

Cited by 16 publications

(10 citation statements)

References 47 publications

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“…To achieve this goal, we have built on existing variational theory (see [18,7]) and discussed an alternate optimization procedure with slack variables and inequality constraints that can address computational limitations within existing techniques. Notably, results within this paper contribute to existing Bayesian statistical literature in [27,29,22] and allow for the study of the latent stochastic behaviour across complex mixed network models, by means of an augmented process for interactions in the resources.…”

Section: Discussionmentioning

confidence: 80%

Variational inference for Markovian queueing networks

Perez

Casale

2021

Adv. Appl. Probab.

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Queueing networks are stochastic systems formed by interconnected resources routing and serving jobs. They induce jump processes with distinctive properties, and find widespread use in inferential tasks. Here, service rates for jobs and potential bottlenecks in the routing mechanism must be estimated from a reduced set of observations. However, this calls for the derivation of complex conditional density representations, over both the stochastic network trajectories and the rates, which is considered an intractable problem. Numerical simulation procedures designed for this purpose do not scale, because of high computational costs; furthermore, variational approaches relying on approximating measures and full independence assumptions are unsuitable. In this paper, we offer a probabilistic interpretation of variational methods applied to inference tasks with queueing networks, and show that approximating measure choices routinely used with jump processes yield ill-defined optimization problems. Yet we demonstrate that it is still possible to enable a variational inferential task, by considering a novel space expansion treatment over an analogous counting process for job transitions. We present and compare exemplary use cases with practical queueing networks, showing that our framework offers an efficient and improved alternative where existing variational or numerically intensive solutions fail.

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Section: Discussionmentioning

confidence: 80%

Variational inference for Markovian queueing networks

Perez

Casale

2021

Adv. Appl. Probab.

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“…To achieve this goal, we have built on existing variational mean-field theory (see Opper and Sanguinetti, 2008;Cohn et al, 2010), and discussed an alternate optimization procedure with slack variables and inequality constraints that can address computational limitations within existing techniques. Notably, results within this paper contribute to existing Bayesian statistical literature in Sutton and Jordan (2011); Wang et al (2016); Perez et al (2017), and first allow for the study of the latent stochastic behaviour across complex mixed network models, by means of an augmented process for interactions in the resources.…”

Section: Discussionmentioning

confidence: 83%

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

Perez,

Casale

2018

Preprint

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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 usually rely on simplifying independence assumptions. In this paper, we present a model augmentation to a multivariate counting process for interactions across service stations, and we first enable the variational evaluation of mean-field measures for partially-observed open and closed multi-class networks. Finally, we show that our approximating framework offers a viable, efficient and improved alternative for inference and uncertainty quantification tasks, where existing variational or numerically intensive solutions do not work.

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“…While the scope of the present note is restricted to exact methods, numerical approximations and asymptotic expansions are also available for G(θ, N ), such as [13,22,24,25,30]. (13)…”

Section: Discussionmentioning

confidence: 99%

A note on integrating products of linear forms over the unit simplex

Casale¹

2017

Preprint

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Integrating a product of linear forms over the unit simplex can be done in polynomial time if the number of variables n is fixed [1]. In this note, we highlight that this problem is equivalent to obtaining the normalizing constant of state probabilities for a popular class of Markov processes used in queueing network theory. In light of this equivalence, we survey existing computational algorithms developed in queueing theory that can be used for exact integration. For example, under some regularity conditions, queueing theory algorithms can exactly integrate a product of linear forms of total degree N by solving N systems of linear equations.

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A Bayesian Approach to Parameter Inference in Queueing Networks

Cited by 16 publications

References 47 publications

Variational inference for Markovian queueing networks

Variational inference for Markovian queueing networks

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

A note on integrating products of linear forms over the unit simplex

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