darkfi/script/research/lotterysim

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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.