Heavy-traffic approximation

As the traffic intensity of a queueing problem approaches 1 (from below), the measures of effectiveness for the system often take on patterns which become essentially insensitive to the exact form of the input and service processes defining the system and, for example, may depend only on expectations and variances. As an illustration, the distribution for line delay of the general G/G/1 queue with utilization rate ρ = 1 − ∈ can be well approximated by W _q(t) = 1 − exp(−at), where a = (1/2)(interarrival time variance + service-time variance)/(mean interarrival time − mean service time). Queueing theory.