An access scheme in a communication system can deal with a mix of devices having different power constraints and different latency requirements and allow highly asymmetric latency behavior. Such a communication system may include a central control station that broadcasts beacon messages on a communication channel, such as a radio channel, and at least one remote terminal that accesses a communication channel based on the beacon messages. The beacon messages are configured such that individual access to the communication channel by each terminal is controlled according to a grouping of the terminals into respective beacon groups. Each beacon group may have a corresponding beacon message, and beacon messages corresponding to different beacon groups may be broadcast at staggered time intervals.