发表机构
Neryva（Neryva公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对异构多服务器队列的反射型UAS，修正其确定性稳定性分析，通过直接CTMC漂移不等式证明策略性能优于UAS与JSSQ。
AI 中文摘要
我们在次临界负载下针对固定参数的异构多服务器队列分析反射型UAS（通用接入调度）路由。确定性替代模型是在非负象限上的反射型常微分方程（ODE），而非无约束漂移方程。该反射型ODE具有唯一的边界平衡点，其特征为标量一致性方程和凸势表示，所有轨迹均收敛至该点。将确定性李雅普诺夫下降法推广至连续时间马尔可夫链（CTMC）稳定性的旧论证不成立：应用于确定性势的精确生成器会产生反射型ODE下降恒等式中不存在的边界项。我们使用加权二次函数为CTMC提供直接的Foster-Lyapunov漂移不等式，绕过失败的推广。在基准参数点，边界平衡点与数值吸引子达到机器精度匹配，且在独立种子块中，默认反射型UAS策略的平均队列长度低于UAS和JSSQ（短作业优先调度）。
英文摘要
We analyze Reflected UAS routing for heterogeneous multi-server queues at fixed parameters under subcritical load. The deterministic surrogate is a reflected ODE on the nonnegative orthant, not the unconstrained drift equation. This reflected ODE has a unique boundary equilibrium characterized by a scalar consistency equation and a convex-potential representation; all trajectories converge to it. The older argument lifting deterministic Lyapunov descent to CTMC stability fails: the exact generator applied to the deterministic potential produces a boundary term absent from the reflected-ODE descent identity. We give a direct Foster-Lyapunov drift inequality for the CTMC using a weighted-quadratic function, bypassing the failed lift. At the benchmark parameter point, the boundary equilibrium matches the numerical attractor to machine precision, and the default Reflected UAS policy has lower mean queue length than UAS and JSSQ across independent seed blocks.
