Hello,
I am a mostly a passive observer in this mailing list, trying to follow
the very interesting discussions and experimenting a bit with running a
node on mainnet (even if I cannot always keep pace with the new
developments due to limited time).
Running a node during the last months inspired some reflections and some
mildly interesting mathematical explorations, which I collected in a
sort of paper which might be of interest to the list:
https://github.com/gr-g/ln-steady-state-model/releases/download/v20190808/Modeling.a.Steady-State.Lightning.Network.Economy.pdf
I say "sort of paper" because there is no bibliography, and no awareness
of the greater context in which these ideas can fit. That said, if
anyone would be interested in making something out of these ideas (e.g.
a real co-authored paper), they are very welcome to do so.
Below is the abstract. Any comment is appreciated!
Best,
Gregorio
Abstract:
In this paper, we consider an idealized scenario in which the Lightning
Network (or any similar payment network) has scaled to the size and
volume of a self-sustained economy, meaning that the number of on-chain
transactions - including channel opening and closing - has become
negligible when compared to the number of off-chain transactions, and
payments continuously flow across a network with relatively stable
topology. We take this scenario to the extreme and model a network where
the channels are fixed, so that payments form a completely closed
system, and where nodes have (on a long enough timescale) stable and
perfectly balanced incoming and outgoing payments (i.e. they spend
exactly what they earn). We call this scenario the "steady-state
economy" of the payment network.
We argue that in such scenario, in a network of /n/ connected nodes,
there is a tendency towards a state where exactly /n/-1 channels have
perfectly balanced flows in the two directions ("self-balancing"
channels), while all other channels are either unused, or have a
permanent tendency towards imbalance: the channel balance accumulates at
one end and the channel is only intermittently available in one
direction ("stuttering" channels). We note that the "self-balancing"
channels form a spanning tree of the network graph, which we call the
"core spanning tree" of the payment network.
We also try to derive some practical lessons from this idealized
scenario, hopefully providing some useful insight to node operators of
the current (embryonic) Lightning Network.
At the end of the paper, we provide some remarks on the more general
case in which nodes do not balance their income and expenses.
https://github.com/gr-g/ln-steady-state-model
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