Comparative Study of Distributed Consensus Gossip Algorithms for Network Size Estimation in Multi-Agent Systems

Martin Kenyeres,Jozef Kenyeres

doi:10.3390/fi13050134

Martin Kenyeres, Jozef Kenyeres

Open Access

https://doi.org/10.3390/fi13050134

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Abstract

Determining the network size is a critical process in numerous areas (e.g., computer science, logistic, epidemiology, social networking services, mathematical modeling, demography, etc.). However, many modern real-world systems are so extensive that measuring their size poses a serious challenge. Therefore, the algorithms for determining/estimating this parameter in an effective manner have been gaining popularity over the past decades. In the paper, we analyze five frequently applied distributed consensus gossip-based algorithms for network size estimation in multi-agent systems (namely, the Randomized gossip algorithm, the Geographic gossip algorithm, the Broadcast gossip algorithm, the Push-Sum protocol, and the Push-Pull protocol). We examine the performance of the mentioned algorithms with bounded execution over random geometric graphs by applying two metrics: the number of sent messages required for consensus achievement and the estimation precision quantified as the median deviation from the real value of the network size. The experimental part consists of two scenarios—the consensus achievement is conditioned by either the values of the inner states or the network size estimates—and, in both scenarios, either the best-connected or the worst-connected agent is chosen as the leader. The goal of this paper is to identify whether all the examined algorithms are applicable to estimating the network size, which algorithm provides the best performance, how the leader selection can affect the performance of the algorithms, and how to most effectively configure the applied stopping criterion.

Highlights

We focus our attention on distributed data aggregation mechanisms, a modern solution preferred in numerous modern applications
There is no significant difference in the values of both applied metrics when the worst-connected agent is selected as the leader instead of the best-connected one
This fact causes that Broadcast gossip algorithm (BG) requires the lowest number of sent messages for consensus achievement, but its estimation precision is so low that this algorithm cannot be applied to estimating the network size—very low precision is achieved in all our experiments

Summary

Introduction

The term “multi-agent system” (MAS) is defined as a computer-based environment formed potentially by hundreds to thousands of interacting intelligent entities referred to as agents [1]. An agent of MAS is considered to be a part of a software/hardware computer-based system that exchanges messages with its peers as well as interacting with its surrounding environment [5,6]. The agents are able to learn novel actions and contexts, thereby being capable to make autonomous decisions [6]. One of the greatest advantages of the agents is their significant flexibility, making MASs applicable in many various fields such as diagnostics, civil engineering, power system restoration, market simulation, network control, etc. An agent of MAS is characterized by other valuable features such as low cost, high efficiency, reliability, etc. An agent of MAS is characterized by other valuable features such as low cost, high efficiency, reliability, etc. and can take various forms—it is a software, 4.0/)

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