In this document, we describe the methodology and the main assumptions used to create the network power model used in the Baseline Crossing project and in the duration multiplier proposal (FIP-0036).
When designing this model, we focus on daily aggregate network dynamics. In order words, we avoid complex simulations that capture individual miner behavior and, instead, model aggregate network metrics and mechanisms using sensible approximations.
With this in mind, the model has the following assumptions:
The model receives the following inputs as parameters:
In other words, these are the "nobs" that the user can tweak to create different scenarios of Storage Providers (SPs) behavior.
Besides these parameters, the model receives some inputs from the current state of the network:
From these inputs, the model derives the raw-byte (RB) power and quality-adjusted (QA) power for each day.
Before we detail how the model computes RB and QA power, we need to define the following notation:
Note that all RB notations have an equivalent notation in QA. As an example, the is defined to be the total QA power at step .
We define the RB power at a given step as the previously observed RB adjusted for the inflows and outflows expected at the current step. The inflows are the new onboards and the renewals, while the outflows are the scheduled expirations:
From the model assumptions, the new onboarded power is simply a constant provided by the user:
The next component is the scheduled expirations. The scheduled power to expire is defined as the sum of the scheduled power to expire coming from two groups of sectors - known active sectors and modeled sectors (i.e., the new onboards and renewals).
We can take the scheduled expirations coming from known active sectors () directly from the network. This is the provided as input.
As for the scheduled expirations coming from the modeled onboards and renewals, we can compute it using the estimated power onboarded, the estimated power renewed, and the sector duration:
Note that if , then by default .
The final component of the RB power equation is the power renewed at step . At the time sectors are expected to expire, a percentage of these sectors will renew. Thus, we estimate renewals simply as the product between the renewal rate and the scheduled expirations:
The renewal rate is user-defined paramater and is a constant ().
The equations for QA power are almost the same as the the ones for RB power, where one can simply exchange the by . There are however two differences.
Firstly, the new onboarded power needs to be adapted to take into account the Fil+ multiplier and the rate of Fil+ deals (where ):
Secondly, the scheduled expirations coming from known sectors are taken directly from the network. This is the provided as input.
The equations for QA power described in the previous section assume that Filcoin Plus deals get a fixed quality multiplier of 10x. To assess the proposal to adapt the quality multipliers, we need a more flexible model that allows the user to change the multiplier and incorporate an additional multiplier based on sector duration.
To design the new equations, we had to make the following assumptions:
Under these assumptions, the equations for the raw-byte power remain unchanged. We only need to update the daily QA power onboarded (as expected!) and QA renewals (since renewed sectors will have a different multiplier based on the sector duration and Fil+ rates).
We should also note that scheduled expirations coming from known active sectors () have the same equation as the "original" QA power section because we assume that active sectors do not change their quality multipliers unless they renew.
The daily quality-adjusted onboarded power is defined as (where ):
Similarly, we need to adapt the renewals equation to take into account the new multiplier after renewal. To do this, it is simpler to start from the scheduled renewals in RB power and apply the new multiplier:
This is in line with the assumption that renewed sectors will have the same Fil+ rate and duration as the new onboarded sectors.