The paper as a pdf can be found on arxiv: https://arxiv.org/abs/1912.09555 in the main folder of this repository you will also find the tex source files:
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
Note that I did some preliminary testing so the interesting code which was used to conduct the simulation, evaluation and experiments is in the vs subfolder of the code folder: https://github.com/renepickhardt/Imbalance-measure-and-proactive-channel-rebalancing-algorithm-for-the-Lightning-Network/tree/master/code/vs
As time was short the code is not in the best shape. I often changed the files from which and to which I saved the data of the experiments by hand and hardcoded when running several experiments. In this why you can't expect to just run the experiments with one command. Yet I think the code is valuable.
The data was taken from the Gossip store of c-lighting. Best to install c-lightning and connect to a node to get your copy of the gossip store (for example you can find my lightning node at https://ln.rene-pickhardt.de )
The network was extracted from gossip and prepared with this script: https://github.com/renepickhardt/Imbalance-measure-and-proactive-channel-rebalancing-algorithm-for-the-Lightning-Network/blob/master/code/extractln.py (run lightning-cli listchannels > channels.json first to have the file)
The results can be found in code/vs/fig at https://github.com/renepickhardt/Imbalance-measure-and-proactive-channel-rebalancing-algorithm-for-the-Lightning-Network/tree/master/code/vs/fig
Feel free to reach out if you need help to manage your lightning nodes or if you plan projects using the lightning network.
If you want to support my work please check out https://tallyco.in/s/lnbook or https://patreon.com/renepickhardt