The paper develops a procedure for sensitivity analysis of the GI/G/m/B queue. m is the number of servers, B is the number of additional waiting places. It calls B the buffer size or capacity. This queue has a renewal arrival process and independent service times. The paper assumes that the service times are identically distributed and their density function f(x) is positive for all x>0. It shows how to estimate the steady-state distribution of the waiting time in the queue for different buffer sizes B by using a single simulation run. The present method is based on the score function (likelihood ratio) methodology. The paper also presents numerical results of simulation experiments.