Whether an idea, information, infection, or innovation diffuses throughout a
society depends not only on the structure of the network of interactions, but
also on the timing of those interactions. Recent studies have shown that
diffusion can fail on a network in which people are only active in "bursts",
active for a while and then silent for a while, but diffusion could succeed on
the same network if people were active in a more random Poisson manner. Those
studies generally consider models in which nodes are active according to the
same random timing process and then ask which timing is optimal. In reality,
people differ widely in their activity patterns -- some are bursty and others
are not. Here we show that, if people differ in their activity patterns, bursty
behavior does not always hurt the diffusion, and in fact having some (but not
all) of the population be bursty significantly helps diffusion. We prove that
maximizing diffusion requires heterogeneous activity patterns across agents,
and the overall maximizing pattern of agents' activity times does not involve
any Poisson behavior