Bayesian Forecasting of WWW Traffic on the Time Varying Poisson Model

Traffic forecasting from past observed traffic data with small calculation complexity is one of important problems for planning of servers and networks. Focusing on World Wide Web (WWW) traffic as fundamental investigation, this paper would deal with Bayesian forecasting of network traffic on the time varying Poisson model from a viewpoint from statistical decision theory. Under this model, we would show that the estimated forecasting value is obtained by simple arithmetic calculation and expresses real WWW traffic well from both theoretical and empirical points of view.

💡 Research Summary

The paper addresses the practical problem of forecasting web traffic with minimal computational overhead, a critical need for capacity planning in servers and networks. It proposes a Bayesian forecasting framework built on a time‑varying Poisson (TVP) model, where the Poisson intensity λt evolves over time according to a multiplicative random walk: λt+1 = λt·εt, with εt drawn from a log‑normal distribution having unit mean and variance σ². By selecting a Gamma prior for λt, the authors exploit the conjugacy between the Gamma distribution and the Poisson likelihood, ensuring that the posterior after each observation remains Gamma‑distributed. The posterior parameters update in closed form: αt+1 = αt + yt and βt+1 = βt + 1, where yt is the observed count at time t.

The forecasting rule is derived from a decision‑theoretic perspective. Under a quadratic loss function, the Bayes estimator that minimizes expected loss is simply the posterior mean E