AI 中文总结
该研究针对具有相关耐心与服务时间、允许服务抢占和弃权的多服务器队列，推导了其测度值流体极限，证明解收敛到闭式不动点，聚焦于实用的抢占式LCFS策略。
AI 中文摘要
我们考虑一个多服务器队列，其中具有一般耐心时间和服务时间的任务以更新过程的形式到达。与标准假设相反，我们允许服务期间的抢占和弃权（不执行），这与电动汽车充电、云计算中的任意时间算法等应用相关。此外，我们不假设耐心时间与服务时间相互独立，而这一直是现有文献中的关键假设。我们使用二维卦限上的离散测度来描述系统状态，其原子的坐标分别代表任务的已获得服务时间和系统内停留时间。在温和假设下，我们推导了当服务器数量趋于无穷大且任务到达率成比例增长时的流体极限。该极限由一个测度值积分输运方程给出，当初始条件为零测度时，我们可显式求解该方程。我们还证明，无论初始条件如何，所有解都收敛到同一个不动点，该不动点具有闭式表达式。我们的结果聚焦于抢占式先来先服务（LCFS）策略，该策略在近期研究中被证实具有实际吸引力。
英文摘要
We consider a many-server queue where tasks with general patience and service times arrive as a renewal process. Contrary to the standard assumptions, we allow for preemption and abandonment during service, relevant in applications such as electric vehicle charging and anytime algorithms in cloud computing. Moreover, we do not assume independence of patience and service times, which has been a critical assumption in the literature. We describe the state of the system using a discrete measure on a two-dimensional orthant, such that the coordinates of its atoms represent the attained service and time in the system of tasks. Under mild assumptions, we derive the fluid limit as the number of servers approaches infinity and the arrival rate of tasks grows proportionally. The limit is given by a measure-valued integral transport equation that we solve explicitly when the initial condition is the null measure. We also prove that all solutions, regardless of the initial condition, converge to the same fixed point, which admits a closed-form expression. Our results focus on the preemptive Last-Come-First-Served (LCFS) policy, which has been identified as practically appealing in recent work.
Comments95 pages
