Variability always occurs to be the most frighteningphenomena in implementation of various kinds of experiments. We desire to control variability and decrease the variance of experiments in order to be aware of the accuracy of the constructed models and consequently supply reliable results. Importance Sampling, also called Biased Sampling is one of the variance reduction techniques especially used in Monte Carlo Methods. This study includes a research to gather the appropriate importance sampling density which gives the lowest variance. We illustrate the importance sampling method on an M/M/1 queuing problem involving a limited waiting capacity of 50 of buffer size and solve it with an efficient C coded simulation program. We first execute naïve simulation, afterwards we carried out importance sampling method and supplied meaningful decrease in the estimated variance of the case which queue length ever exceeds buffer size. By this way, one can calculate any expectation that cannot be calculated by analytically. Numerical results indicate that longer tailed proposal distributions provide much more meaningful decrease.