Optimal Queue Design

TL;DR

This paper investigates the design of optimal queue mechanisms for resource allocation, showing that simple FCFS rules with no additional information are often optimal for incentivizing agents to join and stay in the queue.

Contribution

It introduces a framework for optimal queue design controlling entry, exit, priority, and information, revealing FCFS as a key optimal discipline under mild conditions.

Findings

Optimal mechanisms induce agents to join up to a certain queue length.

FCFS serves as the optimal queue discipline in many scenarios.

No information beyond recommendations is optimal for incentivizing agents.

Abstract

We study the optimal method for rationing scarce resources through a queue system. The designer controls agents' entry into a queue and their exit, their service priority -- or queueing discipline -- as well as their information about queue priorities, while providing them with the incentive to join the queue and, importantly, to stay in the queue, when recommended by the designer. Under a mild condition, the optimal mechanism induces agents to enter up to a certain queue length and never removes any agents from the queue; serves them according to a first-come-first-served (FCFS) rule; and provides them with no information throughout the process beyond the recommendations they receive. FCFS is also necessary for optimality in a rich domain. We identify a novel role for queueing disciplines in regulating agents' beliefs and their dynamic incentives and uncover a hitherto unrecognized virtue of FCFS in this regard.