Bayesian inference for queueing networks and modeling of internet services

TL;DR

This paper introduces a Bayesian approach using MCMC to infer queueing network parameters from incomplete data, enabling performance modeling of large-scale internet services with missing information.

Contribution

It develops a novel Bayesian inference framework for queueing networks with missing data, including a model selection technique, which was not previously addressed in the literature.

Findings

Successfully applied to benchmark web application data

Provides a method for model selection among nested queueing models

Addresses inference challenges with incomplete data in queueing networks

Abstract

Modern Internet services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers. Because these services operate under strict performance requirements, a statistical understanding of their performance is of great practical interest. Such services are modeled by networks of queues, where each queue models one of the computers in the system. A key challenge is that the data are incomplete, because recording detailed information about every request to a heavily used system can require unacceptable overhead. In this paper we develop a Bayesian perspective on queueing models in which the arrival and departure times that are not observed are treated as latent variables. Underlying this viewpoint is the observation that a queueing model defines a deterministic transformation between the data and a set of independent variables called the service times. With this viewpoint in hand, we sample from the posterior distribution over missing data and model parameters using Markov chain Monte Carlo. We evaluate our framework on data from a benchmark Web application. We also present a simple technique for selection among nested queueing models. We are unaware of any previous work that considers inference in networks of queues in the presence of missing data.