The Internet’s complexity restricts analysis or simulation to assess its parameters. Instead, actual measurements provide a reality check. Many statistical measurements of the Internet estimate rare event probabilities. Collection of such statistics renders sampling methods as a primary substitute. Within the context of this inquiry, we have presented the conventional Monte Carlo approach to estimate the Internet event probability. As a variance reduction technique, Importance Sampling is introduced which is a modified Monte Carlo approach resulting in a significant reduction of effort to obtain an accurate estimate. This method works particularly well when estimating the probability of rare events. It has great appeal to use as an efficient sampling scheme for estimating the information server density on the Internet. In this chapter, we have proposed the Importance Sampling approaches to track the prevalence and growth of Web service, where an improved Importance Sampling scheme is introduced. We present a thorough analysis of the sampling approaches. Based on the periodic measurement of the number of active Web servers conducted over the past five years, an exponential growth of the Web is observed and modeled. Also discussed in this chapter is the increasing security concerns on Web servers.
Hybrid importance sampling Monte Carlo approach for yield estimation in circuit design