Designing queues for overloaded waiting lists, by Jacob Leshno

 Here's a paper by Jacob Leshno, with a really creative new contribution to the (venerable) queuing literature. 

Leshno, Jacob D. 2022. "Dynamic Matching in Overloaded Waiting Lists." American Economic Review, December, 112 (12): 3876-3910. DOI: 10.1257/aer.20201111 (ungated working paper link here)

"Abstract: This paper introduces a stylized model to capture distinctive features of waiting list allocation mechanisms. First, agents choose among items with associated expected wait times. Waiting times serve a similar role to that of monetary prices in directing agents' choices and rationing items. Second, the expected wait for an item is endogenously determined and randomly fluctuates over time. We evaluate welfare under these endogenously determined waiting times and find that waiting time fluctuations lead to misallocation and welfare loss. A simple randomized assignment policy can reduce misallocation and increase welfare."

"A practical recommendation is the simple service-in-random order (SIRO) queuing policy. A SIRO buffer-queue mechanism has a simple description: agents who decline an item are allowed to join a priority pool for their preferred item, and agents in each priority pool have an equal probability of receiving an arriving item. We characterize the SIRO buffer-queue mechanism as the robustly optimal mechanism. This simple randomization does not fully equalize the expected wait across states, but it lessens the expected wait fluctuations and therefore reduces the misallocation probability and achieves higher welfare in equilibrium than FCFS." [FCFS= first come first served.]

"In summary, this paper offers two messages for the practical design of allocation through waiting lists. First, although many public-housing authorities have waiting list policies that discourage applicants from declining items, the analysis suggests agents should be encouraged to decline mismatched items. When the system is overloaded, an agent who declines a mismatched item allows the system to search further and assign the item to a matching agent. Furthermore, such an agent reduces the waiting costs of others by allowing them to be assigned before him. Second, equalizing the expected wait agents face when making their choice can improve welfare. This can be achieved by the SIRO buffer-queue mechanism or by partial information mechanisms. Both are practical mechanisms that offer agents more equal options at the time they make their choice, and thus reduce misallocation and improve welfare."