  In Part I \cite{Zhao13TSPasync1}, we introduced a fairly general model for
asynchronous events over adaptive networks including random topologies, random
link failures, random data arrival times, and agents turning on and off
randomly. We performed a stability analysis and established the notable fact
that the network is still able to converge in the mean-square-error sense to
the desired solution. Once stable behavior is guaranteed, it becomes important
to evaluate how fast the iterates converge and how close they get to the
optimal solution. This is a demanding task due to the various asynchronous
events and due to the fact that agents influence each other. In this Part II,
we carry out a detailed analysis of the mean-square-error performance of
asynchronous strategies for solving distributed optimization and adaptation
problems over networks. We derive analytical expressions for the mean-square
convergence rate and the steady-state mean-square-deviation. The expressions
reveal how the various parameters of the asynchronous behavior influence
network performance. In the process, we establish the interesting conclusion
that even under the influence of asynchronous events, all agents in the
adaptive network can still reach an $O(\nu^{1 + \gamma_o'})$ near-agreement
with some $\gamma_o' > 0$ while approaching the desired solution within
$O(\nu)$ accuracy, where $\nu$ is proportional to the small step-size parameter
for adaptation.
