采用模型数据无关控制稳定排队网络
Stabilizing Queuing Networks with Model Data-Independent Control
AI总结：
针对到达率和服务率未知或时变的排队网络，提出仅依赖状态与拓扑的 MDI 控制策略及稳定性判据，并构造达到最大吞吐量的集中式和分散式策略。
摘要：
经典的排队网络控制策略通常依赖于对模型数据（即到达率和服务率）的准确了解。然而，这些数据并非总是可得，而且可能随时间变化。为应对这一挑战，我们考虑一类模型数据无关（MDI）控制策略，其仅依赖流量状态观测和网络拓扑。具体而言，我们关注能够在集中式和分散式策略下稳定多类 Markov 排队网络的 MDI 控制策略。控制动作包括路由、排序和保持。通过扩展路由并构造分段线性测试函数，我们推导出一个易于使用的判据，用于检验给定 MDI 策略下多类网络的稳定性。对于可稳定的多类网络，我们证明存在一种集中式的稳定 MDI 策略。对于可稳定的单类网络，我们进一步证明存在一种分散式的稳定 MDI 策略。此外，在这两种情形下，我们都构造了达到最大吞吐量的显式策略，并给出数值示例来说明结果。
英文摘要：
Classical queuing network control strategies typically rely on accurate knowledge of model data, i.e., arrival and service rates. However, such data are not always available and may be time-variant. To address this challenge, we consider a class of model data-independent (MDI) control policies that only rely on traffic state observation and network topology. Specifically, we focus on the MDI control policies that can stabilize multi-class Markovian queuing networks under centralized and decentralized policies. Control actions include routing, sequencing, and holding. By expanding the routes and constructing piecewise-linear test functions, we derive an easy-to-use criterion to check the stability of a multi-class network under a given MDI policy. For stabilizable multi-class networks, we show that a centralized, stabilizing MDI policy exists. For stabilizable single-class networks, we further show that a decentralized, stabilizing MDI policy exists. In addition, for both settings, we construct explicit policies that attain maximal throughput and present numerical examples to illustrate the results.
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