Abstract: We consider a slotted Gaussian multiple access system where independent arrivals are queued at each transmitter. The arriving packets at each terminal have to delivered to the receiver within a max-delay constraint. An interesting distributed case happens when each transmitter only knows its own arrival process. In this setup, we seek energy efficient transmission schemes minimizing the average sum-power. Optimal schemes are explicitly identified for a unit slot delay constraint, and then extended to general max-delay constraints using an iterative procedure.