Approximating by enhanced interpolation in queueing analyses

It is often difficult to obtain waiting-time measures for non-Markovian, general multi-server queues. Thus there has long been interest in the development of effective approximations for assessing waiting-time behavior in complex waiting-line environments, especially those which can be formulated as variations of the classical queueing network paradigm. As a result, we have developed and extensively tested a procedure for mean delay-time approximation in general multi-server queues by combining the ideas of classical numerical interpolation with major concepts from the classical queueing literature. 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.