Queuing network control allows allocation of scarce resources to manage congestion, a fundamental problem in manufacturing, communications, and healthcare. Compared to standard RL problems, queueing problems are distinguished by unique challenges: i) a system operating in continuous time, ii) high stochasticity, and iii) long horizons over which the system can become unstable (exploding delays). To provide the empirical foundations for methodological development tackling these challenges, we present an open-sourced queueing simulation framework, QGym, that benchmark queueing policies across realistic problem instances. Our modular framework allows the researchers to build on our initial instances, which provide a wide range of environments including parallel servers, criss-cross, tandem, and re-entrant networks, as well as a realistically calibrated hospital queuing system. From these, various policies can be easily tested, including both model-free RL methods and classical queuing policies. Our testbed significantly expands the scope of empirical benchmarking in prior work, and complements thetraditional focus on evaluating algorithms based on mathematical guarantees in idealized settings. QGym code is open-sourced at https://github.com/namkoong-lab/QGym.

We study a seller who sells a single good to multiple bidders with uncertainty over the joint distribution of bidders' valuations, as well as bidders' higher-order beliefs about their opponents. The seller only knows the (possibly asymmetric) means of the marginal distributions of each bidder's valuation and the range. An adversarial nature chooses the worst-case distribution within this ambiguity set along with the worst-case information structure. We find that a second-price auction with a symmetric, random reserve price obtains the optimal revenue guarantee within a broad class of mechanisms we refer to as competitive mechanisms, which include standard auction formats such as the first-price auction. The optimal mechanism possesses two notable characteristics. First, the mechanism treats all bidders identically even in the presence of ex-ante asymmetries. Second, when bidders have identical means and the number of bidders n grows large, the seller's optimal reserve price converges in probability to a non-binding reserve price and the revenue guarantee converges to the mean at rate O(1/n).