Delay guarantee versus throughput in broadcast fading channels

We consider a single-antenna broadcast fading channel with n backlogged users. Assuming the transmission is packet-based, we define the delay as the minimum number of channel uses that guarantees all n users successfully receive m packets. A delay optimal strategy such as round-robin achieves the delay of mn. For the optimal throughput strategy (i.e. transmitting to the user with the best channel condition at each channel use), we derive the mean and variance of the delay for any m and n. For large n, it is proved that the expected delay in receiving the first packet in all users scales like n log n as opposed to n for the round-robin scheduling.