Transition points for non-Gaussian and non-i.i.d. demand processes

Determine the Small Battery Region/Large Battery Region transition points for demand processes other than the i.i.d. Gaussian processes analyzed in the paper, using the relevant demand statistics and temporal correlations.

Background

The paper defines the Small Battery Region (SBR) as the regime in which storage primarily mitigates single-slot demand spikes and the Large Battery Region (LBR) as the regime in which overdraw is caused by sustained multi-slot demand excursions. The transition battery size determines when the ideal linear power-savings relationship ceases to apply and diminishing returns begin.

For i.i.d. Gaussian demand processes, the paper estimates the transition at approximately the midpoint of the no-battery margin. It states that the transition depends on the tail behavior and temporal correlations of the demand process, but does not derive transition points for other demand models. This unresolved problem is relevant to dimensioning storage for workloads with non-Gaussian distributions, multiple modes, or temporal dependence.