A Simple Relationship Between Light and Heavy Traffic Limits

Abstract

Let ρ be the traffic intensity of an open queueing system, and let f(ρ), 0 ≤ ρ < 1 be a function, such as an average queue length or sojourn time. A relationship between the light and heavy traffic limits of f is found that is asymptotically exact for high-order light traffic limits (derivatives at ρ = 0). This simple but unexpected result provides a natural method for approximating f based on partial information. The approximation it provides turns out to be identical to the “canonical” interpolation approximation based on the same partial information. Relationships are then derived that correspond to noncanonical interpolation approximations. These relationships may he useful for gauging the accuracy of interpolation approximations.