Jacknife and Bootstrap Estimation of the Mean Number of Customers in Service for an $M/G/{\infty}$

This thesis studies the estimation from interarrival and service time data of the mean number of customers in service at time t for an $M/G/{\infty}$ queue. The assumption is that the parametric form of the service time distribution is unknown and the empirical distribution of twe service time is used in the estimate the mean number of customers in service. In the case in which the customer arrival rate is known the distribution of the estimate is derived and an approximate normal confidence interval procedure is suggested. The use of the nonparametric methods, which are the jackknife and the bootstrap, to estimate variability and construct confidence intervals for the estimate is also studied both analytically and by simulation.