Optimization in a two-stage multi-server service system with customer priorities

Abstract

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.

Keywords:

• Optimization
• queueing models
• service systems
• work load allocation

Notes

No potential conflict of interest was reported by the authors.