Data-Driven Modeling of Web Traffic Flow Using Functional Modal Regression

Real-time control of web traffic is a critical issue for network operators and service providers. It helps ensure robust service and avoid service interruptions, which has an important financial impact. However, due to the high speed and volume of actual internet traffic, standard multivariate time series models are inadequate for ensuring efficient real-time traffic management. In this paper we introduce a new model for functional time series analysis, developed by combining a local linear smoothing approach with an L1-robust estimator of the quantile’s derivative. It constitutes an alternative, robust estimator for functional modal regression that is adequate to handle the stochastic volatility of high-frequency of web traffic data. The mathematical support of the new model is established under functional dependent case. The asymptotic analysis emphasizes the functional structure of the data, the functional feature of the model, and the stochastic characteristics of the underlying time-varying process. We evaluate the effectiveness of our proposed model using comprehensive simulations and real-data application. The computational results illustrate the superiority of the nonparametric functional model over the existing conventional methods in web traffic modeling.