Timestep length

The simulation calculates the state of the tokenomics sequentially, stepping through time. In general, lower timesteps lead to higher precision but also higher simulation times. In practice, this value usually ranges from a few hours to a few days, with 1 day as the default value.

The end-user of the dashboard can change the time step value. Therefore, the equations must adapt to different possible time step values.

For instance, imagine that we are calculating the amount of fees generated by a value proposition during the current timestep, which we might need to define a token flow. Intuitively, if the timestep was 2 days instead of 1 day, this amount of fees should be (roughly) doubled, since the protocol has had double the time to generate fees.

In practice, this means that in equations where we need to calculate absolute quantities (e.g. a total amount of fees generated during this timestep) from relative quantities (e.g. fees generated per month), we need to multiply the relative quantity by the time step value, in the correct units. This is done in the equations by referencing the timestep variable, which by default is in seconds. In order to normalize the units we can add, in this case, timestep.months, to use it directly in months. If the timestep for the simulation is 1 day, timestep.months will be substituted by the value 0.033333… (that is, 1/30), applying the desired unit conversion.