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

Eman Almehdawe, Beth Jewkes and Qi-Ming He

Journal of the Operational Research Society, 2019, vol. 70, issue 2, 326-337

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.

Date: 2019
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DOI: 10.1080/01605682.2018.1438762

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