On the Scalability and Message Count of Trickle-based Broadcasting Schemes

TL;DR

This paper provides a mathematical analysis of the Trickle broadcasting algorithm in wireless sensor networks, modeling its process with Markov chains, analyzing message count, and proposing a generalized version with adjustable listen-only period.

Contribution

It introduces a Markov chain model for Trickle, analyzes its message count, confirms previous conjectures, and proposes a generalized Trickle with a tunable listen-only period.

Findings

Markov chain model accurately describes Trickle behavior

Stationary distribution of the chain is characterized

Generalized Trickle with adjustable listen-only period is proposed

Abstract

As the use of wireless sensor networks increases, the need for efficient and reliable broadcasting algorithms grows. Ideally, a broadcasting algorithm should have the ability to quickly disseminate data, while keeping the number of transmissions low. In this paper, we analyze the popular Trickle algorithm, which has been proposed as a suitable communication protocol for code maintenance and propagation in wireless sensor networks. We show that the broadcasting process of a network using Trickle can be modeled by a Markov chain and that this chain falls under a class of Markov chains, closely related to residual lifetime distributions. It is then shown that this class of Markov chains admits a stationary distribution of a special form. These results are used to analyze the Trickle algorithm and its message count. Our results prove conjectures made in the literature concerning the effect of a listen-only period. Besides providing a mathematical analysis of the algorithm, we propose a generalized version of Trickle, with an additional parameter defining the length of a listen-only period.