README.md 1.5 KB
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.
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
comparing range of target values between
notice below that both y,T in the pallas field, and simulation have same range.
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.