Service is provided to a set of parallel queues by a single server, The service of queue i may be initiated only at certain time instances {t(n)(i)}(infinity)(n=1) that constitute the connectivity instances for queue i, The service of different customers cannot overlap. Scheduling is required to resolve potential contention of services initiated at closely spaced, closer than the service time, connectivity instances. At any time t, the future connectivity instances are available for scheduling, An anticipative policy is given, which at time t schedules the transmissions until a certain future time t + h, The length of the scheduling horizon h is selected based on the backlog att, The allocation of the server in the interval [t, t + h], is done in accordance to the backlogs of the individual queues at t. The throughput region of the system is characterized, and it is shown that the policy we propose achieves maximum throughput. The policy has a low implementation complexity which is bounded for all the achievable throughput vectors. The average delay and the scheduling complexity are studied by simulation, and the trade-off between the two is demonstrated, The above scheduling problem arises in the access layer of the cross-links of a satellite network.