A Stochastic Model for Popularity Measures in Web Dynamics

In this paper, we propose a stochastic web dynamic model based on the concept of queuing theory to measure popularity of websites in the World Wide Web. We assume that the characteristics of a website such as novelty, popularity, reliability, and relevancy are governed by two major forces: internal or self-growth of each website and external functions acting on the website. In stochastic language, these two forces can be considered as random variables and able to investigate the important characteristics of websites. These characteristics include a probability distribution of the number of visitors to websites, the visiting times distribution, users´ attention, the functional growth and decay of individual websites, the relationship between the dynamics of the web and its structure. We then define and investigate measuring process of popularity of websites using stochastic difference equations based on the structure of the web taken users´ attention into account. For validation, we present some simulation results with the respect to parameter variations in the model. It shows that the proposed model can efficiently and adequately analyze the characteristics and behaviors of websites in web dynamical system.