[Paper Review] Finite Time Exact Quantized Average Consensus with Limited Resources and Transmission Stopping for Energy-Aware Networks

Apostolos I. Rikos, Christoforos N. Hadjicostis+1 more|arXiv (Cornell University)|Oct 1, 2021

Energy Efficient Wireless Sensor Networks4 citations

TL;DR

This paper proposes a novel event-triggered distributed algorithm for finite-time exact quantized average consensus in energy-aware wireless networks. It enables nodes to compute the exact average of initial quantized values in finite time, stop transmitting once consensus is reached, and significantly reduce energy and communication overhead through efficient, adaptive updates on arbitrary strongly connected digraphs.

ABSTRACT

Composed of spatially distributed sensors and actuators that communicate through wireless networks, networked control systems are emerging as a fundamental infrastructure technology in 5G and IoT technologies, including diverse applications, such as autonomous vehicles, UAVs, and various sensing devices. In order to increase flexibility and reduce deployment and maintenance costs, many such applications consider battery-powered or energy-harvesting networks, which bring additional limitations on the energy consumption of the wireless network. Specifically, the operation of battery-powered or energy-harvesting wireless communication networks needs to guarantee (i) efficient communication between nodes and (ii) preservation of available energy. Motivated by these novel requirements, in this paper, we present and analyze a novel distributed average consensus algorithm, which (i) operates exclusively on quantized values (in order to guarantee efficient communication and data storage), and (ii) relies on event-driven updates (in order to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage). We characterize the properties of the proposed algorithm and show that its execution, on any time-invariant and strongly connected digraph, will allow all nodes to reach, in finite time, a common consensus value that is equal to the exact average (represented as the ratio of two quantized values). Furthermore, we show that our algorithm allows each node to cease transmissions once the exact average of the initial quantized values has been reached (in order to preserve its battery energy). Then, we present upper bounds on (i) the number of transmissions and computations each node has to perform during the execution of the algorithm, and (ii) the memory and energy requirements of each node in order for the algorithm to be executed.

Motivation & Objective

• To address energy constraints in battery-powered or energy-harvesting wireless networks used in IoT and 5G applications.
• To enable exact average consensus using only quantized values, avoiding quantization-induced errors.
• To reduce energy consumption by allowing nodes to stop transmitting once consensus is reached.
• To bound the number of transmissions, computations, memory, and energy per node for practical deployment.
• To design a deterministic algorithm that works on any time-invariant, strongly connected directed graph without topological restrictions.

Proposed method

• The algorithm operates exclusively on quantized values, representing the average as a ratio of two integers to ensure exactness.
• It employs event-triggered updates based on three conditions that determine when a node should transmit.
• Each node maintains local state variables and updates them using a distributed rule that ensures convergence to the exact average.
• Transmission stopping is enforced when all nodes satisfy the event-triggering conditions and reach a common value.
• The algorithm is analyzed on arbitrary time-invariant, strongly connected digraphs, with convergence proven in finite time.
• Upper bounds on transmissions, time steps, memory, and energy are derived based on graph size and initial value range.

Experimental results

Research questions

• RQ1 Can a distributed algorithm achieve exact average consensus using only quantized values in finite time?
• RQ2 How can energy consumption be minimized in wireless networks by enabling transmission stopping after consensus?
• RQ3 What are the upper bounds on transmissions, computations, memory, and energy required per node for such an algorithm?
• RQ4 Can the algorithm operate without requiring specific network topologies, such as undirected or balanced graphs?
• RQ5 How does the algorithm perform in practice on random directed graphs with limited resources?

Key findings

• The algorithm achieves finite-time exact quantized average consensus on any time-invariant, strongly connected digraph, with convergence guaranteed in a bounded number of steps.
• In simulations over 1,000 random 20-node digraphs, the average number of time steps to convergence was 103.875, with a maximum of 209 and a minimum of 5.
• The average number of total transmissions across all nodes was 240.547, with a minimum of 103 and a maximum of 368.
• After approximately 210 time steps, the average number of active transmitters dropped to nearly 1, and by step 210, all transmissions ceased as consensus was reached.
• The consensus value was exactly equal to the average of the initial quantized values (e.g., 10.7 in the example), confirming exactness.
• The upper bounds on transmissions and time steps derived in theory were significantly higher than observed in practice, indicating strong practical efficiency.