决策时刻至关重要：揭示其对随机变化连接性调度稳定性的影响
Decision-Epoch Matters: Unveiling its Impact on the Stability of Scheduling with Randomly Varying Connectivity
AI总结：
本文研究了随机连接下并行队列单服务器模型，发现最大稳定区域强烈依赖于决策时刻的定义；在非抢占式设置中稳定区域急剧缩减，而在 $γ$ 决策时刻设置中可通过增大 $γ$ 任意接近无约束设置，并证明 SLC 策略在两种约束设置下均最大稳定。
摘要：
一个经典的排队理论结果指出，在并行队列单服务器模型中，最大稳定区域不依赖于调度决策时刻，并且对于抢占式和非抢占式系统而言是相同的。我们在此考虑每个队列可能连接到服务器或不连接的情况，这取决于一个外生过程。在我们的主要结果中，我们表明最大稳定区域现在强烈依赖于决策时刻的定义方式。我们将可以在任意时刻做出决策的设置（无约束设置）与另外两种设置进行比较：决策要么在离开时刻采取（非抢占式调度），要么在速率为 $γ$ 的指数时钟响起时采取。我们刻画了这两种约束配置的最大稳定区域，从而观察到与无约束配置相比的缩减。在非抢占式设置中，最大稳定区域与无约束设置相比急剧缩减，我们得出结论：非抢占式调度器无法在稳定性方面机会主义地利用随机变化的连接性。相反，对于 $γ$ 决策时刻，我们观察到最大稳定区域在决策时刻的速率 $γ$ 上是单调的，并且如果我们选择足够大的 $γ$，就可以任意接近无约束设置中的最大稳定区域。我们进一步表明，Serve Longest Connected (SLC) 队列在两种约束设置中都是最大稳定的，这适用于在已连接队列中进行选择的一组策略。从方法论的角度来看，我们引入了一种称为“流体极限测试”(TFL) 的新颖理论工具，这可能具有独立的意义。TFL 是一个简单的测试，如果流体极限满足该测试，就允许我们得出稳定性的结论。
英文摘要：
A classical queuing theory result states that in a parallel-queue single-server model, the maximum stability region does not depend on the scheduling decision epochs, and in particular is the same for preemptive and non-preemptive systems. We consider here the case in which each of the queues may be connected to the server or not, depending on an exogenous process. In our main result, we show that the maximum stability region now does strongly depend on how the decision epochs are defined. We compare the setting where decisions can be made at any moment in time (the unconstrained setting), to two other settings: decisions are taken either (i) at moments of a departure (non-preemptive scheduling), or (ii) when an exponentially clock rings with rate $γ$. We characterise the maximum stability region for the two constrained configurations, allowing us to observe a reduction compared to the unconstrained configuration. In the non-preemptive setting, the maximum stability region is drastically reduced compared to the unconstrained setting and we conclude that a non-preemptive scheduler cannot take opportunistically advantage (in terms of stability) of the random varying connectivity. Instead, for the $γ$ decision epochs, we observe that the maximum stability region is monotone in the rate of the decision moments $γ$, and that one can be arbitrarily close to the maximum stability region in the unconstrained setting if we choose $γ$ large enough. We further show that Serve Longest Connected (SLC) queue is maximum stable in both constrained settings, within the set of policies that select a queue among the connected ones. From a methodological viewpoint, we introduce a novel theoretical tool termed a ``test for fluid limits'' (TFL) that might be of independent interest. TFL is a simple test that, if satisfied by the fluid limit, allows us to conclude for stability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
