A fast and accurate iterative solution of a multi-class threshold-based queueing system with hysteresis

In this paper, we consider a K-server multi-class threshold-based queueing system with hysteresis in which the number of servers, employed for servicing customers of each class i, is governed by a forward threshold vector F, = [F, (1), F, (2), •.., Fi(Ki- 1)] and a reverse threshold vector R = [Ri(1), Ri(2),..., Ri(K;- 1)]. There are many applications and systems where a multi-class threshold-based queueing sys-tem can be of great use. One motivation for using threshold-based techniques is that such systems incur significant server setup, usage, and removal costs. And, as in most practical situations, an important concern is not only the system per-formance but rather its cost/performance ratio. The mo-tivation for use of hysteresis is to control the cost during momentary fluctuations in workload. Moreover, servers in such systems are often needed by multiple classes of work-loads, and hence, it is desirable to find good approaches to sharing these serw~rs among the different workloads, prefer-ably without statically partitioning the server pool among the classes; threshold-based techniques constitute one cate-gory of such approaches. Consequently, an important and distinguishing characteristic of our work is that we consider a multi-class system, which is needed in modeling of many applications and systems. Our main goal in this work is to develop an efficient method for solving such models and computing the corresponding performance measures of in-terest, which can subsequently be used in evaluating designs of threshold-based systems. 1