The fluid limit of the multiclass processor sharing queue
The fluid limit of the multiclass processor sharing queue
复制标题
多类处理器共享队列的流量限制
作者：
A. B. Tahar;A. Jean
考虑一个单服务器排队系统，系统中有几类顾客，每类顾客都有自己的更新输入过程和一般服务时间分布。在完成服务时，客户可以离开或重新进入队列，可能作为不同类别的客户。服务器在平等的处理器共享原则下运行。在Gromoll等人（Ann. Appl. Probab. 12：797-859，2002）和Puha等人（Math. Oper. Res. 31（2）：316-350，2006），我们建立了适当归一化的状态过程到由代数和积分方程系统表征的流体极限的收敛。我们证明了这个方程组的唯一解的存在性，无论是一个稳定的和超载的队列。我们还描述了流体极限的轨迹的渐近行为。
Consider a single server queueing system with several classes of customers, each having its own renewal input process and its own general service times distribution. Upon completing service, customers may leave, or re-enter the queue, possibly as customers of a different class. The server is operating under the egalitarian processor sharing discipline. Building on prior work by Gromoll et al. (Ann. Appl. Probab. 12:797–859, 2002) and Puha et al. (Math. Oper. Res. 31(2):316–350, 2006), we establish the convergence of a properly normalized state process to a fluid limit characterized by a system of algebraic and integral equations. We show the existence of a unique solution to this system of equations, both for a stable and an overloaded queue. We also describe the asymptotic behavior of the trajectories of the fluid limit.