Consider a fully connected network of nodes, some of which have a piece of
data to be disseminated to the whole network. We analyze the following
push-type epidemic algorithm: in each push round, every node that has the data,
i.e., every infected node, randomly chooses c∈Z+ other nodes
in the network and transmits, i.e., pushes, the data to them. We write this
round as a random walk whose each step corresponds to a random selection of one
of the infected nodes; this gives recursive formulas for the distribution and
the moments of the number of newly infected nodes in a push round. We use the
formula for the distribution to compute the expected number of rounds so that a
given percentage of the network is infected and continue a numerical comparison
of the push algorithm and the pull algorithm (where the susceptible nodes
randomly choose peers) initiated in an earlier work. We then derive the fluid
and diffusion limits of the random walk as the network size goes to ∞
and deduce a number of properties of the push algorithm: 1) the number of newly
infected nodes in a push round, and the number of random selections needed so
that a given percent of the network is infected, are both asymptotically normal
2) for large networks, starting with a nonzero proportion of infected nodes, a
pull round infects slightly more nodes on average 3) the number of rounds until
a given proportion λ of the network is infected converges to a constant
for almost all λ∈(0,1). Numerical examples for theoretical results
are provided.Comment: 28 pages, 5 figure
