This 2D model reconciles the same mismatch as the 3D terminal — stochastic renewable power feeding a buffer tank that ships drain on a fixed calendar — but drives the renewable side with a genuinely different, independently-computed mechanism: a continuous-time Markov chain (CTMC) over three wind regimes, rather than a mean-reverting diffusion. This is the "Markov-modulated fluid queue" model used in real storage-sizing studies:
states: Calm(0) → Breezy(1) → Gusty(2), linear chain
exit rates R = [r01, r10+r12, r21]·k(variability)
holding time in state i ~ Exponential(Rᵢ) (Gillespie algorithm)
CF(state i) = clip(mean + offsetᵢ, 0, 1), offsets = [−a, 0, +a]
dS/dt = P(t) − D(t), P(t) = Pmax·CF(regime(t))
0 ≤ S(t) ≤ Smax; D(t) = shipload/Tship during a scheduled loading
Because the chain's transition rates all scale together with the variability setting (only the pace of switching changes, not the ratio between them), its stationary distribution is invariant: solving π·Q = 0 for this linear 3-state chain gives π = (1/3, 4/9, 2/9) for (Calm, Breezy, Gusty) regardless of how gusty the wind is — only how fast it swings between states. The long-run mean capacity factor works out to mean − a/9, a small systematic offset from the slider's nominal value that is verified numerically below.
- Mean capacity factor — sets the CTMC's central Breezy state and shifts Calm/Gusty around it.
- Variability — widens the gap between the three regime power levels and speeds up how often the chain switches between them.
- Buffer tank size — larger tanks smooth more variability but cost more capital; the core sizing trade-off.
- Ship interval — how often a fixed-size cargo is drawn from the tank; tighter schedules need proportionally larger buffers.
- Strip chart — scrolls the tank fill level against sim-time, with a coloured band behind it showing which wind regime was active — a view the 3D scene can't show directly.
Real-world relevance: regime-switching (Markov-modulated) models are a standard way energy-storage engineers represent correlated renewable variability — unlike i.i.d. or diffusion noise, they capture the fact that a calm spell tends to persist rather than flipping randomly every instant, which is exactly what drives tank buffer sizing in real green-ammonia export projects.