  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.
