Delay Constrained Scheduling over Fading Channels: Optimal Policies for Monomial Energy-Cost Functions

TL;DR

This paper derives optimal scheduling policies for transmitting a fixed number of bits within a deadline over fading channels, minimizing energy use under convex monomial cost functions without future channel knowledge.

Contribution

It introduces the optimal policies for delay-constrained scheduling with monomial energy-cost functions and explores the dual problem of maximizing transmitted bits under energy constraints.

Findings

Derived the optimal scheduling policy for convex monomial energy costs.

Analyzed the trade-off between channel quality and deadline constraints.

Explored the dual problem of maximizing bits with energy limitations.

Abstract

A point-to-point discrete-time scheduling problem of transmitting $B$ information bits within $T$ hard delay deadline slots is considered assuming that the underlying energy-bit cost function is a convex monomial. The scheduling objective is to minimize the expected energy expenditure while satisfying the deadline constraint based on information about the unserved bits, channel state/statistics, and the remaining time slots to the deadline. At each time slot, the scheduling decision is made without knowledge of future channel state, and thus there is a tension between serving many bits when the current channel is good versus leaving too many bits for the deadline. Under the assumption that no other packet is scheduled concurrently and no outage is allowed, we derive the optimal scheduling policy. Furthermore, we also investigate the dual problem of maximizing the number of transmitted bits over $T$ time slots when subject to an energy constraint.