  The influence of node mobility on the convergence time of averaging gossip
algorithms in networks is studied. It is shown that a small number of fully
mobile nodes can yield a significant decrease in convergence time. A method is
developed for deriving lower bounds on the convergence time by merging nodes
according to their mobility pattern. This method is used to show that if the
agents have one-dimensional mobility in the same direction the convergence time
is improved by at most a constant. Upper bounds are obtained on the convergence
time using techniques from the theory of Markov chains and show that simple
models of mobility can dramatically accelerate gossip as long as the mobility
paths significantly overlap. Simulations verify that different mobility
patterns can have significantly different effects on the convergence of
distributed algorithms.
