A Light Traffic Approximation for a Single-Server Queue
Published Online:1 Nov 1984https://doi.org/10.1287/moor.9.4.624
Abstract
It is shown that in the GI/G/1 queue, with W(S, T) denoting a stationary waiting time random variable that is determined by the generic service and interarrival times S and T,
$$ \lim_{\gamma \rightarrow \infin} EW(S,\gamma T)/E(S - \gamma T)_+ = 1/\mbox{Pr}\{T >0 \} $$
whenever the right-hand side exceeds one. While equality need not necessarily hold when Pr{T > 0} = 1, sufficient conditions are given for the limit result to remain true.
