Stability of Scheduled Message Communication over Degraded Broadcast Channels

TL;DR

This paper analyzes the stability of scheduled message communication over degraded broadcast channels with fading, combining queueing and information theory to characterize achievable message arrival rates and stability conditions.

Contribution

It derives an outer bound for achievable arrival rates, proves the existence of stable stationary policies, and links stability regions to the information-theoretic capacity region.

Findings

Outer bound on achievable message arrival vectors

Existence of stable stationary policies for arrival vectors within the bound

Stability region aligns with the capacity region under certain regimes

Abstract

We consider scheduled message communication over a discrete memoryless degraded broadcast channel. The framework we consider here models both the random message arrivals and the subsequent reliable communication by suitably combining techniques from queueing theory and information theory. The channel from the transmitter to each of the receivers is quasi-static, flat, and with independent fades across the receivers. Requests for message transmissions are assumed to arrive according to an i.i.d. arrival process. Then, (i) we derive an outer bound to the region of message arrival vectors achievable by the class of stationary scheduling policies, (ii) we show for any message arrival vector that satisfies the outerbound, that there exists a stationary ``state-independent'' policy that results in a stable system for the corresponding message arrival process, and (iii) under two asymptotic regimes, we show that the stability region of nat arrival rate vectors has information-theoretic capacity region interpretation.