AI 中文总结
研究为扩散尺度系统开发有色马尔可夫调制布朗运动模型，用于新工作抢占活动层的情况，颜色编码栈位置和优先级，背景阶段控制漂移和波动性，通过反向递归总结偏移，得到平稳乘积形式表示及公式。
AI 中文摘要
我们为扩散尺度系统开发了一个有色马尔可夫调制布朗运动模型。在该模型中，新创建的工作抢占活动层，占据有序栈顶部，且在暂停工作恢复前必须耗尽。这种抢占出现在新工作打断当前活动的情况，如后进先出队列和中断驱动调度。颜色编码栈位置和优先级，背景阶段通过一类转换控制各颜色内的漂移和波动性，二类转换在严格正的随机启动高度创建更高颜色。通过反向递归总结更高颜色偏移，得到平稳乘积形式表示及相关公式。
英文摘要
We develop a colored Markov-modulated Brownian motion model for diffusion-scale systems in which newly created work preempts the active layer, occupies the top of an ordered stack, and must deplete before suspended work resumes. Such preemption arises whenever new work interrupts whatever is currently active, as in last-come, first-served queues and interrupt-driven scheduling, with diffusive dynamics appropriate when the processing rate itself fluctuates randomly. Colors encode stack position and priority, while a background phase, evolving through first-kind transitions that leave the active color unchanged, controls drift and volatility within each color. Second-kind transitions create higher colors at strictly positive random launch heights. A backward recursion summarizes higher-color excursions through return matrices and occupation-density kernels. We obtain stationary product-form representations under hold-and-jump and regulated-base boundary conventions, given explicitly through matrix-analytic formulae, and give matrix-transform formulas for illustrative launch-height families.
