A Light Traffic Approximation for a Single-Server Queue

Source 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, [Formula: see text] 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.