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.ipynb_checkpoints f87435f9ff [research/lotterysim] miscel changes %!s(int64=3) %!d(string=hai) anos
blockchain_scripts bd78bdaa45 [research/lotterysim] reorg lotterysim, acc_staked_ratio plot added %!s(int64=3) %!d(string=hai) anos
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reports fe1c82bec0 [research/lotterysim/reports] update cascade report with simulation params, change title %!s(int64=3) %!d(string=hai) anos
search_space dee4a65777 [research/lotterysim] merge controllers %!s(int64=3) %!d(string=hai) anos
README.md bd78bdaa45 [research/lotterysim] reorg lotterysim, acc_staked_ratio plot added %!s(int64=3) %!d(string=hai) anos
__init__.py bd78bdaa45 [research/lotterysim] reorg lotterysim, acc_staked_ratio plot added %!s(int64=3) %!d(string=hai) anos
acc_vs_staked_ratio.py 6916f7c4c1 [research/lotterysim/reports] finalize report %!s(int64=3) %!d(string=hai) anos
discrete_instance.py 6916f7c4c1 [research/lotterysim/reports] finalize report %!s(int64=3) %!d(string=hai) anos
draw.py bd78bdaa45 [research/lotterysim] reorg lotterysim, acc_staked_ratio plot added %!s(int64=3) %!d(string=hai) anos
playground.ipynb f87435f9ff [research/lotterysim] miscel changes %!s(int64=3) %!d(string=hai) anos
primary_discrete_auto_crawler.py 6916f7c4c1 [research/lotterysim/reports] finalize report %!s(int64=3) %!d(string=hai) anos
secondary_discrete_auto_crawler.py 2f497332f9 [research/lotterysim] replace apy with apr %!s(int64=3) %!d(string=hai) anos
secondary_takahashi_auto_crawler.py 2f497332f9 [research/lotterysim] replace apy with apr %!s(int64=3) %!d(string=hai) anos
takahashi_instance.py 2f497332f9 [research/lotterysim] replace apy with apr %!s(int64=3) %!d(string=hai) anos

README.md

title: darkfi lottery simulation author: ertosns

date: 11/1/2023

simulate darkfi consensus lottery with a discrete controller

discrete pid controller.

control lottery f tunning paramter

$$f[k] = f[k-1] + K_1e[k] + K_2e[k-1] + K_3e[k-2]$$

with $k_1 = k_p + K_i + K_d$, $k_2 = -K_p -2K_d$, $k_3 = K_d$, and e is the error function.

simulation criterion

find $K_p$, $k_i$, $K_d$ for highest accuracy running the simulation on N trials, of random number of nodes, starting with random airdrop (that all sum to total network stake), running for random runing time.

alt text

notice that best parameters are spread out in the search space, picking the highest of which, and running the simulation, running for 600 slots, result in with >36% accuracy

alt text

comparing range of target values between

notice below that both y,T in the pallas field, and simulation have same range.

alt text

conclusion

using discrete controller the lottery accuracy > 33% with randomized number of nodes, and randomized relative stake. can be coupled with khonsu^1 to achieve 100% accuracy and instant finality.