Fluid Limits for Multiple-Input Shortest Remaining Processing Time Queues
研究了采用最短剩余处理时间策略的多输入排队系统，建立了流体模型并证明其作为系统一阶近似的极限定理，适用于分析高负载下的响应时间。
A single queueing station serving K input streams with renewal arrivals and generally distributed independent and identically distributed service times is considered. Customers are served by the Shortest Remaining Processing Time policy. In the case of a tie, the first-in, first-out policy is utilized. We analyze a fluid model for the evolution of a measure-valued state descriptor of this system, with particular emphasis on its limiting behavior in the critical case as time gets large. We also prove a fluid limit theorem justifying our fluid model as the first-order approximation of the queueing system under consideration. Along the way, we establish fluid limits for the corresponding state-dependent response times.