Optimal least-squares approximations to the transient behavior of the stable M/M/1 queue

We present simple exponential approximations to the transient behavior of the stable M/M/1 queue. The approximations are optimal in a least-squares sense, and we find them to agree well with exact results. Our approach can be used to derive approximations for any time-dependent quantity with a known Laplace transform, e.g., the probability distribution and the moments of the queue size, of the waiting time, etc. It is the only approach we are aware of in which the error between approximations and exact results can be explicitly computed.<>