Technical Note—A Last Word on <i>L</i> = λ<i>W</i>

Abstract

This note gives a rigorous proof of the queuing formula L = λW, using as hypotheses only that the limiting averages, λ and W, exist and are finite. The proof is related to one given in a previous paper by the author that used a discounted analogue and Tauberian theorems. The proof in the present paper, however, is direct and avoids the use of transforms. Some comments are offered on the relation between the proof and the heuristic arguments for L = λW commonly encountered in the literature.