A queuing analysis based on Internet traffic measurements is provided. First a finite-size Pareto queuing model for the heavy-tailed behavior of Internet flow traffic is presented. The derivation of the flow blocking probability with a finite buffer based on Internet flow traffic is provided. The flow blocking probability is given as a function of the buffer size, system load and parameter /spl alpha/ of the measured flow duration distribution. These results are very useful for design trade-off of admission control algorithm or general network engineering where heavy tail phenomenon exists. In addition the behavior of the Internet consecutive packet loss duration (outage duration) is studied. The implicit relationship between heavy tail flow duration and heavy tail outage duration is identified in the queuing aspect.