Infinitesimal Perturbation Analysis Estimates for Moments of the System Time of an M/M/1 Queue

We consider infinitesimal perturbation analysis estimates for the derivative of moments of the system time in an M/M/1 queue in steady state. The unbiasedness of these estimates is established for derivatives with respect to the mean service time and the arrival rate. A similar result is obtained for the system time of the ith customer in a GI/G/1 queue with fixed initial conditions.