A single server is assigned to M parallel queues with independent Poisson arrivals. Service times are constant, but the server has the opportunity to initiate service at a given queue only at times forming a Poisson process. Four related scheduling policies are investigated. a) A simple first-come, first-serve policy for which the stability region is determined, b) A policy with maximum throughput, but requiring the server to have advance knowledge of service opportunities, c) A policy of threshold type, which is shown to be optimal among nonlookahead policies with preemption, and d) An adaptive policy, which when M = 2 is shown to provide stability for all arrival rate vectors for which stability is possible under any nonlookahead policy with preemption. The work is motivated by the problem of transmission scheduling for a packet-switched, low-altitude, multiple satellite system.