  As the use of wireless sensor networks increases, the need for
(energy-)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 develop a model
describing the message count in large-scale wireless sensor networks. We focus
our attention on the popular Trickle algorithm, which has been proposed as a
suitable communication protocol for code maintenance and propagation in
wireless sensor networks. 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. This generalization
proves to be useful for optimizing the design and usage of the algorithm. For
single-cell networks we show how the message count increases with the size of
the network and how this depends on the Trickle parameters. Furthermore, we
derive distributions of inter-broadcasting times and investigate their
asymptotic behavior. Our results prove conjectures made in the literature
concerning the effect of a listen-only period. Additionally, we develop an
approximation for the expected number of transmissions in multi-cell networks.
All results are validated by simulations.
