Queues with Redundancy: Is Waiting in Multiple Lines Fair?

• 成果类型: Article
• 署名作者: Nageswaran, Leela; Scheller-Wolf, Alan
• 署名单位: University of Washington; University of Washington Seattle; Carnegie Mellon University
• 刊物名称: M&SOM-MANUFACTURING & SERVICE OPERATIONS MANAGEMENT
• ISSN/ISSBN: 1523-4614
• DOI: 10.1287/msom.2021.1052
• 发表日期: 2022
• 页码: 1959-1976
• 关键词: Service Operations; queuing theory; stochastic methods

摘要

Problem definition: We study service systems where some (so-called redundant) customers join multiple queues simultaneously, enabling them to receive service in any one of the queues, while other customers join a single queue. Academic/practical relevance: The improvement in overall system performance due to redundant customers has been established in prior work. We address the question of fairness- whether the benefit experienced by redundant customers adversely affects others who can only join a single line. This question is particularly relevant to organ transplantation, as critics have contended that multiple listing provides unfair access to organs for patients based on wealth. Methodology: We analyze two queues serving two classes of customers; the redundant class joins both queues, whereas the nonredundant class joins a single queue randomly. We compare this system against a benchmark wherein the redundant class resorts to joining the shortest queue (JSQ) if multiple queue joining were not allowed, capturing the most likely case if multilisting was prohibited: Affluent patients could still afford to list in the region with the shorter wait list. Results: We prove that when the arrival rate of nonredundant customers is balanced across both queues, they actually benefit under redundancy of the other class-that is, redundancy is fair. We also establish that redundancy may be unfair under some circumstances: Nonredundant customers are worse off if their arrival rate is strongly skewed toward one of the queues. We illustrate how these findings apply in the organ-transplantation setting through a numerical study using publicly available data. Managerial implications: Our analysis helps identify when, and by how much, multiple listing may be unfair and, as such, could be a useful tool for policy makers who may be concerned with trying to ensure equitable access to resources, such as organs, across patients with differing wealth levels.