OPTIMAL LEAST-SQUARES APPROXIMATIONS TO THE TRANSIENT-BEHAVIOR OF THESTABLE 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 q uantity with a known Laplace transform, e.g., the probability distribu tion and the moments of the queue size, of the waiting time, etc. It i s the only approach we are aware of in which the error between approxi mations and exact results can be explicitly computed.