A simple approximation for modeling nonstationary queues

Evaluation of the behavior of queues with nonstationary arrival processes is of importance in several applications including communication networks. However, the analysis of nonstationary queues is in general computationally complex and seldom produces closed form expressions. Thus approximation methods may be more appropriate. The pointwise stationary fluid flow approximation (PSFFA) for determining the mean queue length of nonstationary queues is presented. The PSFFA combines steady state queueing results with a simple fluid flow model to develop a single nonlinear differential equation model of the queue. Numerical integration techniques are used to solve the PSFFA model and the method is illustrated by several examples. The power of this approach is that it can handle very general queueing systems.