修正了异构队列中反射UAS的稳定性分析，证明其收敛性并提升性能。
Reflected UAS: Corrected Deterministic Stability and Direct CTMC Drift Calculation
- 用反射常微分方程建模，刻画队列边界平衡点
- 在基准参数下，均值队列长度优于UAS和JSSQ
- 首次直接给出连续时间马尔可夫链的漂移不等式
我们分析了在次临界负载下固定参数的异构多服务器队列中的反射UAS路由。确定性近似为非负象限上的反射常微分方程（ODE），而非无约束漂移方程。该反射ODE具有唯一边界平衡点，由标量一致性方程和凸势函数表示；所有轨迹均收敛于此。旧有将确定性李雅普诺夫下降推广至连续时间马尔可夫链（CTMC）稳定性的论证失效：对确定性势函数应用精确生成元时，出现原反射ODE下降恒等式中缺失的边界项。本文通过加权二次函数，直接建立了CTMC的福斯特-李雅普诺夫漂移不等式，绕过失败的推广。在基准参数点，边界平衡点与数值吸引子精确匹配至机器精度，且默认反射UAS策略在独立种子块上均表现出低于UAS和JSSQ的平均队列长度。
原文摘要 · Abstract (English)
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.
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