Computation offloading expands the range of computationally-intensive and latency-constrained tasks that mobile users can execute. In a multi-user setting, the system selects the offloading users and allocates resources to them so that the overall energy consumption is minimized. We show herein that when the users have different latencies, the appropriate signalling architecture has a time-slotted structure with different subsets of the offloading users transmitting in each time slot. Furthermore, for multiple access schemes that exploit the full capabilities of the channel we analytically determine the optimal signalling architecture and we develop a highly-efficient algorithm for the power and rate allocations in each time slot. Our numerical results illustrate the advantages of the proposed system over those that employ a single-slot architecture and over time division multiple access.