Volunteer convergence refers to the influx of volunteers to affected areas after large‐scale disasters. There are not only many benefits to volunteer convergence, but it also creates significant logistical challenges that can impede relief efforts. This study examines polices for admitting volunteers into organized relief operations, and for assigning admitted volunteers to relief tasks. We represent this problem as a queueing system where, in addition to customer arrivals and departures, random server arrivals and abandonments are also present. Then, using a Markov decision process framework, we analyze server admission and assignment policies that seek to minimize relief tasks holding costs as well as volunteer holding and rejection costs. We show that the classic cμ rule, a server allocation policy that determines where to put servers based on relief tasks holding costs and processing requirements, is optimal under both collaborative and non‐collaborative service regimes and when batch server arrivals are allowed. Additionally, we find that the optimal server admission policy is a complex state‐dependent policy. As a result, we propose a class of admission heuristics that depend on the number of workers in the system and the remaining system workload. In a numerical study, we show that our heuristic policies perform well with respect to long‐run average costs, waiting times, number of volunteers in the system, and number of volunteers idling in the system over a range of parameter values and distributions that are based on real data from a case study. As such, they promise volunteer coordinators an effective and simple way to manage disaster volunteers.