On Erasure Broadcast Channels with Hard Deadlines

Abstract: This paper considers packet scheduling over a broadcast channel with packet erasures to multiple receivers with different messages (multiple uni-cast) each with possibly different hard deadline constraints. A novel metric is proposed and evaluated: the global deadline outage probability, which gives the probability that the hard communication deadline is not met for at least one of the receivers. The cut-set upper bound is derived and a scheduling policy is proposed to determine which receiver's packets should be sent in each time slot. This policy is shown to be optimal among all scheduling policies, i.e., it achieves all boundary points of cut-set upper bounds when the transmitter knows the erasure patterns for all the receivers ahead of making the scheduling decision. An expression for the global deadline outage probability is obtained for two receivers and is plotted and interpreted for various system parameters. These plots are not Monte-Carlo simulations, and hence the obtained expression may be used in the design of future downlink broadcast networks. Future extensions to per-user deadline outage probabilities as well as to scenarios with causal knowledge of the channel states are briefly discussed.