The traffic on the internet has known to be heavy tailed: the size of file transfers through FTP or HTTP applications, as well as those transferred by P2P applications has been observed to have a very heavy tail. Typically modeled as Pareto distributed with parameter between 1.05 to 1.5, the file size has infinite variance. This is the source of many difficulties in simulating data traffic: convergence is very slow, simulations have to be very long, and the standard methods for deriving confidence intervals, based on the CLT, are not applicable here. We illustrate these well known problems through the simulation study of a processor sharing queue, which is often used to model session level resource sharing in the internet. We test bootstrap methods to accelerate convergence and improve the precision of simulations, and test a direct approach to obtain confidence interval based on the histogram of the empirical distributions. The conclusion drawn are then compared to those obtained when simulating in ns2 data transfer using TCP