The study of rational queueing has a long and distinguished history focused on individuals' preference to avoid waiting. Surprisingly, there are settings in which some potential arrivals (which we also refer to as requests) derive utility from waiting and disutility from service. Our primary example is the U.S. affirmative asylum process. In this context, applicants obtain a work permit while waiting for an asylum interview; hence, if the (expected) wait is long enough, then even an applicant who knows that their application will be denied and lead to deportation proceedings, may find it in their interest to apply and thus benefit from legally working during the wait. Similar dynamics could occur in other settings like content moderation in social networks.

The dedicated docket was introduced by the Biden Administration to expedite the processing of asylum claims. It creates a separate queue for immigration proceedings where judges are supposed to issue a decision for each asylum case within a target timeframe. The administration announced the docket with the goals of speed, accuracy, and fairness. Though the program meets its first goal, legal advocacy groups report that this comes at the expense of the last. Referring to it as a "Denial of justice", they find that cases on the dedicated docket routinely fail to access legal representation, and have a much lower asylum grant rate. We aim to understand the operational implication of the dedicated docket. In our stylized queueing model, a policy maker (PM) routes asylees to either the regular or the dedicated docket, and sets a delay target for the dedicated one. Constrained by the target, the court allocates its limited capacity to minimize the average delay. Immigration lawyers schedule their time between dockets to maximize the rate of successful asylum cases.

Queueing systems are widely applicable stochastic models with use cases in communication networks, healthcare, service systems, etc. Although their optimal control has been extensively studied, most existing approaches assume perfect knowledge of the system parameters. Of course, this assumption rarely holds in practice where there is parameter uncertainty, thus motivating a recent line of work on bandit learning for queueing systems. This nascent stream of research focuses on the asymptotic performance of the proposed algorithms. In this paper, we argue that an asymptotic metric, which focuses on late-stage performance, is insufficient to capture the intrinsic statistical complexity of learning in queueing systems which typically occurs in the early stage. Instead, we propose the *Cost of Learning in Queueing (CLQ)*, a new metric that quantifies the maximum increase in time-averaged queue length caused by parameter uncertainty. We characterize the CLQ of a single-queue multi-server system, and then extend these results to multi-queue multi-server systems and networks of queues. In establishing our results, we propose a unified analysis framework for CLQ that bridges Lyapunov and bandit analysis, provides guarantees for a wide range of algorithms, and could be of independent interest.

Ensuring that refugees and asylum seekers thrive (e.g., find employment) in their host countries is a profound humanitarian goal, and a primary driver of employment is the geographic location to which the refugee or asylum seeker is assigned. In the past few years, innovations in analytics have given rise to machine learning (ML) models that predict integration outcomes using personal characteristics. With these ML models, recent research has proposed and implemented algorithms that assign refugees and asylum seekers to geographic locations in a manner that maximizes the average employment. While these algorithms can have substantial overall positive impact (up to 50% increases in average employment rate compared with current practice), using data from two industry collaborators we show that the impact of these algorithms can vary widely across key subgroups based on country of origin, age, or educational background.

We study decentralized multi-agent learning in bipartite queuing systems, a standard model for service systems. In particular, N agents request service from K servers in a fully decentralized way, i.e, by running the same algorithm without communication. Previous decentralized algorithms are restricted to symmetric systems, have performance that is degrading exponentially in the number of servers, require communication through shared randomness and unique agent identities, and are computationally demanding. In contrast, we provide a simple learning algorithm that, when run decentrally by each agent, leads the queueing system to have efficient performance in general asymmetric bipartite queuing systems while also having additional robustness properties. Along the way, we provide the first UCB-based algorithm for the centralized case of the problem, which resolves an open question by Krishnasamy et al.

In this paper, we establish a theoretical comparison between the asymptotic mean square errors of double Q-learning and Q-learning. Our result builds upon an analysis for linear stochastic approximation based on Lyapunov equations and applies to both tabular setting or with linear function approximation, provided that the optimal policy is unique and the algorithms converge. We show that the asymptotic mean-square error of Double Q-learning is exactly equal to that of Q-learning if Double Q-learning uses twice the learning rate of Q-learning and the output of Double Q-learning is the average of its two estimators. We also present some practical implications of this theoretical observation using simulations.