具有贪婪近视服务的空间轮询系统的稳定性
Stability of a spatial polling system with greedy myopic service
摘要：
本文研究了一个圆形的空间排队系统，由一个近视的服务器在随机位置进行轮询，该服务器只能观察有界邻域中的客户。服务器根据贪婪策略进行操作，始终为其邻域中最近的客户提供服务，并且在邻域为空的轮询时刻保持系统不变。该系统被建模为一个测量值的随机过程，这是一个自然的稳定性条件下，不依赖于服务器的扫描范围是正经常性的。当插值次数为轻尾时，证明了稳定系统是几何遍历的。使用数值模拟和启发式光交通近似的系统的稳态行为进行了简要讨论。
英文摘要：
This paper studies a spatial queueing system on a circle, polled at random locations by a myopic server that can only observe customers in a bounded neighborhood. The server operates according to a greedy policy, always serving the nearest customer in its neighborhood, and leaving the system unchanged at polling instants where the neighborhood is empty. This system is modeled as a measure-valued random process, which is shown to be positive recurrent under a natural stability condition that does not depend on the server's scan range. When the interpolling times are light-tailed, the stable system is shown to be geometrically ergodic. The steady-state behavior of the system is briefly discussed using numerical simulations and a heuristic light-traffic approximation.
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