队列网络中去中心化路由的信号机制
Signaling for Decentralized Routing in a Queueing Network
AI总结：
研究双服务站和双控制器的离散时间去中心化路由问题，通过信号机制优化持有成本，提出基于共同信息的阈值策略。
摘要：
在由两个服务站和两个控制器组成的服务系统中，研究了离散时间去中心化路由问题。每个控制器与一个站关联，每个站有无限缓冲区。每个站的外源客户以速率λ到达，服务速率μ。控制器可将等待队列中的客户路由至另一站。控制器完全了解自身站的队列长度，并观察到自身站的外源到达及另一站发送的客户。初始时，每个控制器有对方站客户数的概率质量函数（PMF），且为共同知识。每个时间点，由于等待客户产生持有成本。目标是确定两个控制器的路由策略，以最小化有限时间 horizon 的总预期持有成本或无限时间 horizon 的平均成本。此问题隐含通信；控制器通过路由决定向另一站传递信息，称为信号。尽管信号复杂，证明最优策略由基于共同信息的阈值策略描述。
英文摘要：
A discrete-time decentralized routing problem in a service system consisting of two service stations and two controllers is investigated. Each controller is affiliated with one station. Each station has an infinite size buffer. Exogenous customer arrivals at each station occur with rate $λ$. Service times at each station have rate $μ$. At any time, a controller can route one of the customers waiting in its own station to the other station. Each controller knows perfectly the queue length in its own station and observes the exogenous arrivals to its own station as well as the arrivals of customers sent from the other station. At the beginning, each controller has a probability mass function (PMF) on the number of customers in the other station. These PMFs are common knowledge between the two controllers. At each time a holding cost is incurred at each station due to the customers waiting at that station. The objective is to determine routing policies for the two controllers that minimize either the total expected holding cost over a finite horizon or the average cost per unit time over an infinite horizon. In this problem there is implicit communication between the two controllers; whenever a controller decides to send or not to send a customer from its own station to the other station it communicates information about its queue length to the other station. This implicit communication through control actions is referred to as signaling in decentralized control. Signaling results in complex communication and decision problems. In spite of the complexity of signaling involved, it is shown that an optimal signaling strategy is described by a threshold policy which depends on the common information between the two controllers; this threshold policy is explicitly determined.
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