[Paper Review] Approximate Bayesian inference with queueing networks and coupled jump processes.

Iker Perez, Giuliano Casale|arXiv (Cornell University)|Jul 23, 2018

Markov Chains and Monte Carlo Methods18 references3 citations

TL;DR

This paper introduces a scalable variational Bayesian framework for approximate inference in queueing networks, addressing transient uncertainty quantification in open and closed systems with diverse service disciplines. By leveraging model augmentation and stochastic approximation, it enables efficient inference where traditional methods fail due to computational complexity.

ABSTRACT

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.

Motivation & Objective

• To address the lack of effective transient inference and uncertainty quantification methods in queueing networks despite their widespread use in performance evaluation.
• To overcome computational challenges arising from complex Markov jump processes in queueing systems, which hinder traditional Bayesian inference.
• To develop a flexible and scalable variational inference approach applicable to both open and closed queueing networks with varied service disciplines and priorities.
• To validate the framework on real-world uncertainty quantification tasks involving network service rates.

Proposed method

• The method employs model augmentation over an approximating network system to simplify the posterior structure and enable tractable inference.
• It introduces a variational Bayesian framework that approximates the intractable posterior distribution using a tractable variational family.
• The framework is designed to handle general-form queueing systems, including both open and closed networks with arbitrary service disciplines and priority rules.
• Stochastic approximation techniques are used to optimize the variational parameters, ensuring scalability and convergence.
• The approach leverages the structure of queueing networks to define efficient, structured variational distributions that respect the underlying dynamics.

Experimental results

Research questions

• RQ1 How can approximate Bayesian inference be effectively applied to transient queueing network models with complex dynamics?
• RQ2 What scalable and flexible inference framework can handle both open and closed queueing systems with diverse service disciplines?
• RQ3 How can uncertainty in network service rates be quantified using Bayesian methods in the presence of computational intractability?
• RQ4 To what extent does the proposed variational framework maintain accuracy while improving computational efficiency compared to exact methods?

Key findings

• The proposed variational Bayesian framework enables scalable and flexible inference in complex queueing networks where exact methods are computationally infeasible.
• The model augmentation strategy effectively simplifies the posterior while preserving key system dynamics and uncertainty characteristics.
• The framework successfully quantifies uncertainty in network service rates, demonstrating practical utility in performance evaluation tasks.
• The approach maintains accuracy across diverse service disciplines and priority rules, showing robustness to structural variations in queueing systems.