Scheduling servers in a two-stage queue with abandonments and costs

作     者：Zayas-Caban, Gabriel Cochran, Amy L. 

作者机构：Univ Wisconsin BerbeeWalsh Dept Emergency Med Ind & Syst Engn Madison WI 53705 USA Univ Wisconsin Dept Math Populat Hlth Sci Madison WI USA 

出 版 物：《PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES》 (工程与信息科学中的概率)

年 卷 期：2023年第37卷第3期

页      面：833-851页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0714[理学-统计学（可授理学、经济学学位）] 

主　　题：Operations research Queueing theory Stochastic dynamic programming Stochastic modeling 

摘      要：We consider the assignment of servers to two phases of service in a two-stage tandem queueing system when customers can abandon from each stage of service. New jobs arrive at both stations. Jobs arriving at station 1 may go through both phases of service and jobs arriving at station 2 may go through only one phase of service. Stage-dependent holding and lump-sum abandonment costs are incurred. Continuous-time Markov decision process formulations are developed that minimize discounted expected and long-run average costs. Because uniformization is not possible, we use the continuous-time framework and sample path arguments to analyze control policies. Our main results are conditions under which priority rules are optimal for the single-server model. We then propose and evaluate threshold policies for allocating one or more servers between the two stages in a numerical study. These policies prioritize a phase of service before switching to the other phase when total congestion exceeds a certain number. Results provide insight into how to adjust the switching rule to significantly reduce costs for specific input parameters as well as more general multi-server situations when neither preemption or abandonments are allowed during service and service and abandonment times are not exponential.