[Paper Review] Gaussian process regression as a predictive model for Quality-of-Service in Web service systems

Jakub M. Tomczak, Jerzy Świątek+1 more|arXiv (Cornell University)|Jul 30, 2012

Gaussian Processes and Bayesian Inference25 references3 citations

TL;DR

This paper proposes Gaussian process regression (GPR) with a linear kernel as a probabilistic predictive model for Quality-of-Service (QoS) attributes—such as latency—in Web service systems. It models the relationship between input request streams and QoS outcomes using a non-parametric Bayesian approach, demonstrating statistically significant improvements in prediction accuracy over CART, with p-values of 1.84×10⁻⁵ (MAE) and 0.018 (MSE).

ABSTRACT

In this paper, we present the Gaussian process regression as the predictive model for Quality-of-Service (QoS) attributes in Web service systems. The goal is to predict performance of the execution system expressed as QoS attributes given existing execution system, service repository, and inputs, e.g., streams of requests. In order to evaluate the performance of Gaussian process regression the simulation environment was developed. Two quality indexes were used, namely, Mean Absolute Error and Mean Squared Error. The results obtained within the experiment show that the Gaussian process performed the best with linear kernel and statistically significantly better comparing to Classification and Regression Trees (CART) method.

Motivation & Objective

• To address the gap between theoretical performance prediction models and practical applications in Web service systems.
• To develop a predictive model for QoS attributes—such as latency—based on input request streams and system configurations.
• To evaluate the performance of Gaussian process regression against traditional methods like CART in a controlled simulation environment.
• To provide a probabilistic, non-parametric framework that accounts for uncertainty in system behavior due to internal noise and unknown processes.
• To support optimization tasks such as dynamic resource allocation and service selection through accurate QoS prediction.

Proposed method

• Formulates QoS prediction as a non-parametric regression problem using Gaussian processes, where the function f is drawn from a Gaussian process prior with zero mean and kernel function k(x, x’).
• Models the observed QoS output y as y = f(x) + ε, where ε is zero-mean Gaussian noise with precision β⁻¹.
• Employs type 2 maximum likelihood estimation to learn hyperparameters of the kernel function and noise variance from training data.
• Uses three kernel functions: linear, squared exponential, and a complex kernel combining linear and squared exponential components.
• Develops a custom simulation environment to generate synthetic Web traffic with multiple demand classes, using Poisson processes and lognormal-distributed request sizes.
• Implements a Round Robin scheduler to simulate execution of demands, with fixed execution rates per demand class per time unit.

Experimental results

Research questions

• RQ1 Can Gaussian process regression effectively predict QoS attributes such as latency in Web service systems given input request streams?
• RQ2 How does the performance of Gaussian process regression compare to CART in terms of prediction accuracy for QoS attributes?
• RQ3 Which kernel function (linear, squared exponential, or complex) yields the best predictive performance in the context of Web service QoS modeling?
• RQ4 Is the improvement of Gaussian process regression over CART statistically significant?
• RQ5 Can the proposed simulation environment accurately model real-world Web service behavior for reliable performance evaluation?

Key findings

• Gaussian process regression with a linear kernel achieved the lowest Mean Absolute Error (MAE) and Mean Squared Error (MSE) among all tested models.
• The linear kernel outperformed both the squared exponential and complex kernels in predicting QoS attributes, indicating better modeling of input similarity.
• The complex kernel, being a sum of linear and squared exponential components, performed slightly better than the squared exponential kernel alone.
• A two-sample t-test showed that the difference in MAE between GPR (linear kernel) and CART was statistically significant, with a p-value of 1.84×10⁻⁵.
• For MSE, the difference between GPR (linear kernel) and CART was also statistically significant at the 5% significance level, with a p-value of 0.018.
• The simulation environment successfully generated realistic Web traffic patterns and enabled reliable evaluation of predictive models under controlled conditions.