On Erasure Broadcast Channels with Hard Deadlines

TL;DR

This paper introduces a new scheduling policy for broadcast channels with packet erasures and hard deadlines, optimizing the probability of meeting all deadlines and providing analytical expressions useful for network design.

Contribution

It proposes a novel scheduling policy that is proven optimal for erasure broadcast channels with hard deadlines, and derives explicit outage probability expressions for system analysis.

Findings

The proposed policy achieves all boundary points of the cut-set upper bounds.

An explicit expression for global deadline outage probability is derived for two receivers.

The results can inform the design of future downlink broadcast networks.

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.