Optimal surplus capacity utilization in polling systems via fluid models

Ayush Rawal, V. Kavitha, Manu K. Gupta
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引用次数: 13

Abstract

We discuss the idea of differential fairness in polling systems. One such example scenario is: primary customers demand certain Quality of Service (QoS) and the idea is to utilize the surplus server capacity to serve a secondary class of customers. We use achievable region approach for this. Towards this, we consider a two queue polling system and study its `approximate achievable region' using a new class of delay priority kind of schedulers. We obtain this approximate region, via a limit polling system with fluid queues. The approximation is accurate in the limit when the arrival rates and the service rates converge towards infinity while maintaining the load factor and the ratio of arrival rates fixed. We show that the set of proposed schedulers and the exhaustive schedulers form a complete class: every point in the region is achieved by one of those schedulers. It is well known that exhaustive service policy optimizes system performances like unfinished work. In this paper, we show that it is also optimal from the perspective of individual queues. We further pose two constrained optimization problems: a) admission control, wherein the arrival rates of secondary customers is optimally designed; b) maximizing the revenue considering the losses when secondary arrival rate is fixed. We finally show that exhaustive service discipline at each queue turns out to be optimal.
基于流体模型的轮询系统剩余产能最优利用
我们讨论了投票系统中差异公平性的概念。一个这样的场景示例是:主要客户要求一定的服务质量(QoS),其想法是利用剩余的服务器容量为次要客户提供服务。我们使用可实现区域法。为此,我们考虑了一个双队列轮询系统,并使用一类新的延迟优先级调度器研究了它的“近似可达区域”。我们通过一个具有流体队列的极限轮询系统得到了这个近似区域。在保持负荷系数和到达率比不变的情况下,到达率和服务率趋近于无穷大的极限下,近似是准确的。我们证明了提议的调度程序集和穷举调度程序构成了一个完整的类:区域中的每个点都由其中一个调度程序实现。众所周知,穷举服务策略优化系统性能就像优化未完成的工作一样。在本文中,我们从单个队列的角度证明了它也是最优的。我们进一步提出了两个约束优化问题:a)准入控制,其中二级顾客到达率的优化设计;B)当二次到达率固定时,考虑损失,收益最大化。最后,我们证明了每个队列的穷举服务规则是最优的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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