Delay-Optimal and Energy-Efficient Communications with Markovian Arrivals

TL;DR

This paper investigates the optimal balance between delay and energy consumption in communication systems with Markovian traffic, proposing a cross-layer, threshold-based strategy that adapts to channel and queue states for improved efficiency.

Contribution

It introduces a novel cross-layer approach using CMDP and LP to derive optimal delay-power tradeoffs and develops a threshold-based adaptive transmission algorithm without prior traffic statistics.

Findings

Optimal delay-power tradeoff characterized for Markovian arrivals.

Threshold-based transmission strategy proven optimal.

Algorithm developed for real-time adaptation without prior statistics.

Abstract

In this paper, delay-optimal and energy-efficient communication is studied for a single link under Markov random arrivals. We present the optimal tradeoff between delay and power over Additive White Gaussian Noise (AWGN) channels and extend the optimal tradeoff for block fading channels. Under time-correlated traffic arrivals, we develop a cross-layer solution that jointly considers the arrival rate, the queue length, and the channel state in order to minimize the average delay subject to a power constraint. For this purpose, we formulate the average delay and power problem as a Constrained Markov Decision Process (CMDP). Based on steady-state analysis for the CMDP, a Linear Programming (LP) problem is formulated to obtain the optimal delay-power tradeoff. We further show the optimal transmission strategy using a Lagrangian relaxation technique. Specifically, the optimal adaptive transmission is shown to have a threshold type of structure, where the thresholds on the queue length are presented for different transmission rates under the given arrival rates and channel states. By exploiting the result, we develop a threshold-based algorithm to efficiently obtain the optimal delay-power tradeoff. We show how a trajectory-sampling version of the proposed algorithm can be developed without the prior need of arrival statistics.