A Data Propagation Model for Wireless Gossiping

Wireless sensor networks require communication protocols for efficiently propagating data in a distributed fashion. The Trickle algorithm is a popular protocol serving as the basis for many of the current standard communication protocols. In this paper we develop a mathematical model describing how Trickle propagates new data across a network consisting of nodes placed on a line. The model is analyzed and asymptotic results on the hop count and end-to-end delay distributions in terms of the Trickle parameters and network density are given. Additionally, we show that by only a small modification of the Trickle algorithm the expected end-to-end delay can be greatly decreased. Lastly, we demonstrate how one can derive the exact hop count and end-to-end delay distributions for small network sizes.