Applying variance performance measures for variable service-rate queueing simulation models

Service times in variable-rate service processes depend on the state of a system, e.g. number in queue. This behavior is quite common, but is oftentimes overlooked in simulation models. This paper describes modeling variable-rate queueing systems and the need for different performance measures. The standard performance measures for simple queueing models (the average number in queue, the average wait time, and the average server utilization) describe nicely the long-term steady-state average performance of a system, but they do not describe the time-varying response of a system, and they are not effective for more complex queueing simulation models that incorporate rate-adjustment feedback. Since variable-rate queueing simulation models can adjust the service rate based on the number in queue, they can easily achieve the target average number in queue by applying sufficient rate adjustments. Performance measures for variable-rate models should also consider the variability remaining in the system with the control effort applied. This paper studies two measures of variability of the number in queue, since variability reduction is often the key driver in a lean six-sigma improvement project to improve performance.