Approximating by enhanced interpolation in queueing analyses

Queueing theorists have long made productive use of major concepts from applied mathematics. However, the familiar numerical technique of interpolation, with its great variety of possible interpolation functions, has seen incomplete use in the modeling of delay phenomena. In this work, we show that interpolation has very broad application in the process of deriving approximate results. We study the properties of interpolation approximations for the G/G/c queue and develop a desired analytic framework for such approximations. This structure is then used to derive a simple approximation for the mean queue delay for G/G/c. The approximation contains three key elements: a light-traffic parameter, a heavy-traffic parameter, and a drift parameter that specifically allows the introduction of external data into the approximation.