  Making a payment in a privacy-aware payment channel network is achieved by
trying several payment paths until one succeeds. With a large network, such as
the Lightning Network, a completion of a single payment can take up to several
minutes. We introduce a network imbalance measure and formulate the
optimization problem of improving the balance of the network as a sequence of
rebalancing operations of the funds within the channels along circular paths
within the network. As the funds and balances of channels are not globally
known, we introduce a greedy heuristic with which every node despite the
uncertainty can improve its own local balance. In an empirical simulation on a
recent snapshot of the Lightning Network we demonstrate that the imbalance
distribution of the network has a Kolmogorov-Smirnoff distance of 0.74 in
comparison to the imbalance distribution after the heuristic is applied. We
further show that the success rate of a single unit payment increases from
11.2% on the imbalanced network to 98.3% in the balanced network. Similarly,
the median possible payment size across all pairs of participants increases
from 0 to 0.5 mBTC for initial routing attempts on the cheapest possible path.
We provide an empirical evidence that routing fees should be dropped for
proactive rebalancing operations. Executing 4 different strategies for
selecting rebalancing cycles lead to similar results indicating that a
collaborative approach within the friend of a friend network might be
preferable from a practical point of view
