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Variational inference for Markovian queueing networks

Part of: Markov processes

Published online by Cambridge University Press:  08 October 2021

Iker Perez Open the ORCID record for Iker Perez [Opens in a new window]  and
Giuliano Casale
Iker Perez*
Affiliation:
University of Nottingham
Giuliano Casale*
Affiliation:
Imperial College London
*
*Postal address: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
**Postal address: Department of Computing, Imperial College London, London SW7 2RH, United Kingdom.
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Abstract

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.

Keywords

Queueing networksvariational methodsMarkov jump process

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J28: Applications of continuous-time Markov processes on discrete state spaces
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 3 , September 2021 , pp. 687 - 715
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Copyright
© The Author(s) 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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