Asymptotically Optimal Policies for Hard-deadline Scheduling over Fading Channels

TL;DR

This paper investigates optimal scheduling policies for transmitting a fixed number of bits within a deadline over a fading channel, deriving asymptotic optimal policies in various regimes and comparing their energy efficiency.

Contribution

It introduces asymptotically optimal policies for hard-deadline scheduling over fading channels in different limiting regimes, filling a gap where no closed-form solutions were previously known.

Findings

Optimal policies are identified for large B with fixed T.

Optimal policies are identified for small B with fixed T.

Optimal policies are identified when B and T both grow large.

Abstract

A hard-deadline, opportunistic scheduling problem in which $B$ bits must be transmitted within $T$ time-slots over a time-varying channel is studied: the transmitter must decide how many bits to serve in each slot based on knowledge of the current channel but without knowledge of the channel in future slots, with the objective of minimizing expected transmission energy. In order to focus on the effects of delay and fading, we assume that no other packets are scheduled simultaneously and no outage is considered. We also assume that the scheduler can transmit at capacity where the underlying noise channel is Gaussian such that the energy-bit relation is a Shannon-type exponential function. No closed form solution for the optimal policy is known for this problem, which is naturally formulated as a finite-horizon dynamic program, but three different policies are shown to be optimal in the limiting regimes where $T$ is fixed and $B$ is large, $T$ is fixed and $B$ is small, and where $B$ and $T$ are simultaneously taken to infinity. In addition, the advantage of optimal scheduling is quantified relative to a non-opportunistic (i.e., channel-blind) equal-bit policy.