Abstract As a multi-class variant of the classical egalitarian processor-sharing (EPS) discipline, discriminatory processor sharing (DPS) provides a suitable paradigm to model systems where share exists to control the service access of heterogeneous jobs. Although DPS is a more fine-grained scheduling discipline than EPS, the behavior of closed queueing networks (QNs) with DPS remains poorly understood. We propose in this paper a fluid approach to transient and steady-state analysis of closed QNs comprising delay and DPS stations. Our reference model features an arbitrary routing topology, phase-type service time distributions and class switching. The proposed approach has been validated against simulation for both transient and steady-state analysis. Moreover, we introduce a refined method for approximating response time distributions at either station or system level through transient analysis, showing its improvement upon prior art in handling non-exponentially distributed service times.

中文翻译：

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具有判别处理器共享的封闭排队网络的流体逼近

摘要 作为经典平均处理器共享 (EPS) 规则的多类变体，歧视性处理器共享 (DPS) 提供了一种合适的范式来模拟存在共享以控制异构作业的服务访问的系统。尽管 DPS 是比 EPS 更细粒度的调度规则，但对具有 DPS 的封闭排队网络 (QN) 的行为仍知之甚少。我们在本文中提出了一种对包含延迟站和 DPS 站的封闭 QN 进行瞬态和稳态分析的流体方法。我们的参考模型具有任意路由拓扑、阶段类型服务时间分布和类切换。所提出的方法已经针对瞬态和稳态分析的仿真进行了验证。而且，