发表机构
European Molecular Biology Laboratory; University of Toronto（欧洲分子生物学实验室; 多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究仅可在离散审查周期起始时刻变更服务器分配的多类队列调度问题，分析价值函数对审查周期长度的敏感性，揭示审查周期长短对价值函数单调性的影响及随机性的作用。
AI 中文摘要
随机队列网络的最优控制通常在连续时间控制下进行研究，但在许多服务场景中，管理者仅能在离散且可能不频繁的审查时刻调整决策。本文研究一类多类队列调度问题，其中服务器分配仅可在离散审查周期的起始时刻变更，分析性能如何依赖审查周期长度。我们研究由审查周期长度参数化的一系列关联流体控制问题，刻画价值函数的一阶与二阶敏感性；针对两类情形，推导这些导数的显式表达式并确定其符号。研究发现，在审查周期较短时，价值函数未必单调；当审查周期足够长后，价值函数变为非递减，可能呈现凸或线性区域，最终变为凹函数。我们进一步对原始随机调度问题数值检验上述结论的鲁棒性，结果显示随机性会在较小尺度上平滑非单调性，但定性敏感性模式仍清晰可见，且随系统规模增大而愈发显著。
英文摘要
Optimal control of queueing networks is typically studied under continuous-time control. In many service settings, however, managers can adjust decisions only at discrete and potentially infrequent review epochs. We study a multiclass queue scheduling problem in which server assignments can be changed only at the beginning of discrete review periods, and examine how performance depends on the review-period length. We analyze a family of associated fluid control problems parameterized by the review-period length and characterize the first- and second-order sensitivity of the value function. For the two-class case, we derive explicit expressions for these derivatives and characterize their signs. We find that for short review periods, the value function need not be monotone. Once the review period is sufficiently large, the value function becomes monotone nondecreasing and may exhibit a convex or linear region before eventually becoming concave. These results provide insights on when the value of more frequent control, or \emph{flexibility} with respect to server assignments, is higher. We further numerically examine the robustness of these observations for the original stochastic scheduling problem and show that stochasticity smooths the nonmonotonicity at smaller scales, while the qualitative sensitivity patterns remain visible and become more pronounced as the scale of the system increases.
