AI 中文总结
本文解决了多类比例处理器共享队列（含弃权（不执行）及一般分布）的扩散近似问题，通过推广流体极限并证明扩散缩放下的紧性与唯一性，刻画了由高斯片驱动的随机微分方程系统。
AI 中文摘要
本文解决了具有一般分布且含弃权（不执行）的处理器共享队列的扩散近似这一长期未解问题。具体而言，我们首先将已知的单类含弃权（不执行）处理器共享队列的流体极限推广到多类比例处理器共享队列（含弃权（不执行））。我们证明了流体模型解的唯一性，以及流体缩放模型收敛到流体模型解。接下来，我们证明在扩散缩放下，模型是紧的，并且子序列极限可由一个由高斯片驱动的特定随机微分方程系统唯一刻画，该系统定义在 $\R_+^2$ 上，具有非平凡的协变结构。
英文摘要
In this paper, we resolve the long open problem of the diffusion approximation for a generally distributed processor sharing queue with reneging. In particular, we first extend the known fluid limit for a single class processor sharing queue with reneging to the multiclass proportional processor sharing queue with reneging. We prove uniqueness of fluid model solutions and convergence of fluid scaled models to fluid model solutions. Next, we show that, under diffusion-scaling, the models are tight, and that subsequential limits can be uniquely characterized by a certain system of SDEs driven by a Gaussian sheet on $\R_+^2$ with a nontrivial covariation structure.
