Techniques for allocating event offsets within a period of transmission are described. A mains-powered device (MPD) may act as a “parent” to one or more battery-powered devices (BPDs). The MPD may assign “event offsets” to each BPD. The event offset is a time by which the BPD's timeslot is “offset” from the start of a periodic cycle of transmissions by the MPD. Thus, each event offset indicates a time that the BPD must be “awake,” i.e., operating its radio receiver and/or performing other functionality. A BPD may spend a substantial fraction of its time in a “sleep” mode, wherein less power is used and fewer functions are performed than during a period of that BPD's event offset. Another BPD may have a different event offset. Communications by the MPD with each child BPD may be substantially uniformly distributed over the period. To increase efficiency, groups of BPDs may receive multicasts.