Auxiliary variables for Bayesian inference in multi-class queueing networks

Abstract

Queueing networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the present paper, we focus on the underlying continuoustime Markov chains induced by these networks, and we present a flexible method for drawing parameter inference in multi-class Markovian cases with switching and different service disciplines. The approach is directed towards the inferential problem with missing data, where transition paths of individual tasks among the queues are often unknown. The paper introduces a slice sampling technique with mappings to the measurable space of task transitions between the service stations. This can address time and tractability issues in computational procedures, handle prior system knowledge and overcome common restrictions on service rates across existing inferential frameworks. Finally, the proposed algorithm is validated on synthetic data and applied to a real data set, obtained from a service delivery tasking tool implemented in two university hospitals.

Performance Modelling and Optimisation of NoSQL Database Systems

“…For example, although more challenging mathematically, methods that exploit observed response time distributions have been proposed to address this shortcoming [SCBK15]. However, the applicability of these techniques is often limited by their scalability, as they can require a numerical solution to the underpinning queueing models using rather computationally-intensive approaches such as absorbing Markov chains or fluid differential equations and non-linear optimisation [KPSCD09,PHK17].…”

“…Class-switching has received a limited degree of attention in prior work on demand estimation, possibly with the exception of [PHK17] which considers it in the context of a single multi-server resource. However, workflows arise commonly in distributed systems composed by multiple resources, which is the case we consider in this work.…”

Variational inference for Markovian queueing networks

“…Yet algorithms may be hard to implement, computationally demanding, or applicable only to reduced classes of problems. In the case of QNs, strong temporal dependencies in the stochastic trajectories X impose hard coupling properties amongst rates and paths [27], which limits the applicability of state-of-the-art numerical solutions to the simplest types of network evaluation problems [22]. Alternatively, the complex integrals in (5) may be approximated through a variational approach, where we suitably parametrize an alternative approximating measure to P that will decompose the integrand into multiple independent and analytically tractable parts.…”

“…, o K , the distribution over λ admits a density carried by the Lebesgue measure μ λ , so that dP λ|o 1 ,...,o K = f λ|o 1 ,...,o K dμ λ . In this simple example, numerical MCMC procedures [22] or basic generatormatrix exponentiations combined with a forward-backward algorithm [32] can offer such density approximations; however, this is reportedly very inefficient when N is large. Moreover, in involved networks/processes for complex applications (see next example), such alternatives are simply unusable (i.e.…”

SD: A Divergence-Based Estimation Method for Service Demands in Cloud Systems

“…Class-switching has received a limited degree of attention in prior work on demand estimation, possibly with the exception of [4] which considers it in the context of a single multi-server resource. However, workflows arise commonly in distributed systems composed by multiple resources, which is the case we consider in this work.…”