When prices are fixed, queues become central allocation mechanisms. Yet decentralized waiting queues are often unobserved, creating inefficiencies and the opportunity for informal access through referral networks. This paper studies a 2016 reform in Quebec, Canada, that introduced a centralized system for allocating medical referrals from general practitioners to physician specialists. We find that centralization significantly reduced new specialist consultations. We also infer physician referral networks and estimate a structural model that enables us to conclude that specialists tend to defer consultations for patients referred by general practitioners from whom they receive an unusually large number of referrals.