5 research outputs found
Information Spreading in Stationary Markovian Evolving Graphs
Markovian evolving graphs are dynamic-graph models where the links among a
fixed set of nodes change during time according to an arbitrary Markovian rule.
They are extremely general and they can well describe important dynamic-network
scenarios.
We study the speed of information spreading in the "stationary phase" by
analyzing the completion time of the "flooding mechanism". We prove a general
theorem that establishes an upper bound on flooding time in any stationary
Markovian evolving graph in terms of its node-expansion properties.
We apply our theorem in two natural and relevant cases of such dynamic
graphs. "Geometric Markovian evolving graphs" where the Markovian behaviour is
yielded by "n" mobile radio stations, with fixed transmission radius, that
perform independent random walks over a square region of the plane.
"Edge-Markovian evolving graphs" where the probability of existence of any edge
at time "t" depends on the existence (or not) of the same edge at time "t-1".
In both cases, the obtained upper bounds hold "with high probability" and
they are nearly tight. In fact, they turn out to be tight for a large range of
the values of the input parameters. As for geometric Markovian evolving graphs,
our result represents the first analytical upper bound for flooding time on a
class of concrete mobile networks.Comment: 16 page
Information Propagation Speed in Mobile and Delay Tolerant Networks
The goal of this paper is to increase our understanding of the fundamental
performance limits of mobile and Delay Tolerant Networks (DTNs), where
end-to-end multi-hop paths may not exist and communication routes may only be
available through time and mobility. We use analytical tools to derive generic
theoretical upper bounds for the information propagation speed in large scale
mobile and intermittently connected networks. In other words, we upper-bound
the optimal performance, in terms of delay, that can be achieved using any
routing algorithm. We then show how our analysis can be applied to specific
mobility and graph models to obtain specific analytical estimates. In
particular, in two-dimensional networks, when nodes move at a maximum speed
and their density is small (the network is sparse and surely
disconnected), we prove that the information propagation speed is upper bounded
by ( in the random way-point model, while it is upper bounded by
for other mobility models (random walk, Brownian motion).
We also present simulations that confirm the validity of the bounds in these
scenarios. Finally, we generalize our results to one-dimensional and
three-dimensional networks