A Proof for the Queuing Formula: L = λW
- 1 June 1961
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Operations Research
- Vol. 9 (3) , 383-387
- https://doi.org/10.1287/opre.9.3.383
Abstract
In a queuing process, let 1/λ be the mean time between the arrivals of two consecutive units, L be the mean number of units in the system, and W be the mean time spent by a unit in the system. It is shown that, if the three means are finite and the corresponding stochastic processes strictly stationary, and, if the arrival process is metrically transitive with nonzero mean, then L = λW.Keywords
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