We study a multiclass many-server queueing system with renewal arrivals and generally distributed service and patience times under a nonpreemptive allocation policy. The status of the system is described by a pair of measure-valued processes to track the residual service and patience times of customers in each class. We establish fluid approximations and study the long-term behavior of the fluid model. The equilibrium state of the fluid model leads to a nonlinear program, which enables us to identify a lower bound for the long-run expected total holding and abandonment costs and design an allocation policy to achieve this lower bound. The optimality of the proposed policy is also demonstrated via numerical experiments.

中文翻译：

---

放弃的多服务器队列的虚拟分配策略

我们研究了一种基于非抢占分配策略的具有更新到达时间以及普遍分布的服务和耐心时间的多类多服务器排队系统。系统的状态由一对评估值的过程描述，以跟踪每个类别中客户的剩余服务和耐心时间。我们建立流体近似值并研究流体模型的长期行为。流体模型的平衡状态导致出现非线性程序，这使我们能够为长期预期总持有和放弃成本确定下限，并设计分配策略以实现该下限。还通过数值实验证明了所提出策略的最优性。