NTU queueing with heterogeneous values in non-fluid (canonical) models

Develop an analysis of the Non-Transferable Utility (NTU) canonical M/M/1 queueing model with Poisson arrivals of buyers and items that allows buyers to have heterogeneous values, and characterize the feasible stationary allocations together with the optimal mechanism comprising admissions control, priority rules, and information policy in the non-fluid setting.

Background

The paper surveys queue-based NTU mechanisms and shows that screening via waiting can be analyzed cleanly in a fluid limit, where randomness vanishes and waiting times are deterministically pinned down by Little’s law. In this tractable fluid setting, the authors derive sharp results for allocative efficiency and welfare, including complete pooling under a decreasing inverse hazard rate.

However, the authors note that the canonical (non-fluid) queueing environment—an M/M/1 system with stochastic integer-valued states—poses substantial challenges when buyers’ values are heterogeneous. Feasible allocations of waiting times, admissions, and priority must respect stationary balance constraints over a complex state space, making characterization difficult. They explicitly highlight the absence of NTU analyses that accommodate value heterogeneity in this canonical non-fluid setup and call it an open area.