HPC Eco Race

Below you will see the equation we use to collect the hours/kWh number. We want to have this documented with a notes section to discuss the choices made.

For the below math:
    $ \alpha_c $ = Consumed Core Hours
    $ \alpha_g $ = Consumed GPU Hours
    $ \kappa $ = kWh
    $ \theta_h $ = Percent of the kWh that is HVAC related
    $ \rho_r $ = Percent of the kWh that is generated through renewable sources (Hydro, Solar, Wind, Nuclear, Geothermal, etc.)
    $ \tau $ = The time period for your kWh and CPU/GPU hours measurements (please use the same)

Here is the formula: $$ EcoRaceScore = \Large \frac{(\frac{\alpha_c+\alpha_g}{(\kappa*(100-\theta_h))*(100-\rho_r)})}{\tau} $$

Notes

1. We want an idea of the number of core/gpu hours but have to decided between available vs. consumed. We can surface a few possibilities to study these. Consider a system running at 99% usage. That would be nearly identical in both cases. Now consider one running at 50% usage. If we used the available number we would not see all of the wasted idle hours that were not used. In order to expose them, we have to use consumed hours.
2. CPU and GPU Hours are weighted the same and there were concerns about the GPU hours since there is usually more than one GPU per node. The cores could have the same problem.
3. A rank like this can be weighted any way we want. So we take kWh and multiply by the % that is not kWh (see 3, below) and the % that is sustainable (see 4, below).
4. We wanted to handle the kWh that are HVAC related separately since capabilities are different worldwide and we want to focus on clusters.
5. We wanted to handle the kWh that are generated through sustainabile resources separately since a 100% hydro system should be valued much more highly than a coal or oil system.