Queues with Redundancy: Is Waiting in Multiple Lines Fair?

Abstract

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.