Queues with Redundancy : Is Waiting in Multiple Lines Fair?

In service settings such as multiple listing for organ transplants and supermarkets with multiple checkout lines, some customers join multiple queues simultaneously, enabling them to receive service in any one of the queues. We study fairness in these systems: Does such multiple queue-joining behavior benefit or harm those who do not do so? We analyze two queues serving two classes of customers, one (so-called “redundant”) class joins both queues while the other (“non-redundant”) 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 case if multi-listing was prohibited: affluent patients could still afford to list in the region with the shorter wait list. We prove that when the arrival rate of non-redundant customers is balanced across both queues, they benefit under redundancy of the other class, i.e., redundancy is fair. We also establish that redundancy may be unfair under some circumstances: Non-redundant 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. 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 organs across patients with differing wealth levels