Jc. Bolot et Au. Shankar, OPTIMAL LEAST-SQUARES APPROXIMATIONS TO THE TRANSIENT-BEHAVIOR OF THESTABLE M M/1 QUEUE/, IEEE transactions on communications, 43(2-4), 1995, pp. 1293-1298
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.