We consider a two-user energy harvesting broadcast channel, and characterize the delay minimal transmission policies that minimize the total delay experienced by the data packets in the system. We consider a continuous time system where the delay experienced by each bit is given by the time spent by the bit in the queue waiting to be transmitted to its receiver. We consider the case where all data packets are available at the transmitter at the beginning of the communication session. We characterize the optimal solution in terms of the Lagrange multipliers, and present an iterative algorithm that optimally calculates their values. Our results show that in the optimal policy, both users may not be served simultaneously all the time; there may be times where only the strong user or only the weak user is served alone. We also show that the optimal policy may have gaps in transmission where none of the users is served until the next energy arrival.
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