Optimization in a two-stage multi-server service system with customer priorities
研究了两阶段多服务器排队系统中两类顾客的优先权问题，提出了近似方案和迭代算法来最小化高优先顾客的阻塞延迟，并应用于急救医疗和航空公司人员配置。
We consider a two-stage, multi-server queueing network that serves two types of customers, which we refer to as type a and type b. Type a customers require service at both sequential stages and type b customers only require service at the second stage. The first stage has one node and the second stage has multiple nodes. Type a customers possess a higher non-pre-emptive priority than type b customers. Depending on the model application, two goals are explored: the first goal is to allocate type a customers to the second- stage nodes in a manner that minimizes the average blocking delay; the second goal is to optimize the service speed of each server in the second stage so that the average blocking delay experienced by type a customers is minimized. In this paper, we develop an approximation scheme and an iterative algorithm to find stationary policies, which we then apply to the real-world contexts of Emergency Medical Services planning and airline staffing. Numerical examples show that, compared to some typical heuristic schemes (e.g., proportional allocation based on arrival/service capacity), the suggested allocation policies result in type a customers experiencing shorter delays and allow more of them receive service.