Bounding of performance measures for threshold-based queuing systems: Theory and application to dynamic resource management in video-on-demand servers

In this paper, we consider a K-server threshold-based queuing system with hysteresis in which the number of active servers is governed by a forward threshold vector F = (F-1, F-2,...,FK-1) (where F-1 < F-2 < (...) < FK-1) and a reverse threshold vector R = (R-1, R-2,...,RK-1) (where R-1 < R-2 < (...) < RK-1). There are many applications where a threshold-based queuing system can be of great use. The main motivation for using a threshold-based approach in such applications is that they incur significant server setup, usage, and removal costs. As in most practical situations, an important concern is not only the system performance, but rather its cost/performance ratio. The motivation for use of hysteresis is to control the cost during momentary fluctuations in workload. An important and distinguishing characteristic of our work is that, in our model, we consider the time to add a server to be nonnegligible. This is a more accurate model, for many applications, than previously considered in other works. Our goal in this work is to develop an efficient method for computing the steady state probabilities of a multiserver threshold-based queuing system with hysteresis, which will, in turn, allow computation of various performance measures. We also illustrate how to apply this methodology in evaluation of the performance of a Video-on-Demand (VOD) storage server which dynamically manages its I/O resources.