The station's consumable buffer B(t) drains at a noisy daily rate and is refilled by discrete cargo launches. This is a continuous-review (s, Q) inventory policy: an order for a fixed quantity Q is placed the instant the buffer crosses reorder point s, and arrives after a stochastic lead time L.
dB/dt = -μ · (1 + ε), ε ~ noise
if B ≤ s and no order in flight: place order for Q
order arrives at t + L, L = L0 + jitter (σ, truncated uniform)
on arrival: B ← B + Q
The reorder point must cover expected demand during the lead time plus a safety margin. The risk of running dry before the next delivery arrives is estimated with the classic safety-stock (newsvendor) formula, using the normal CDF Φ:
expected demand during lead time: D_L = μ · L0
demand std-dev during lead time: σ_L = σ_ε · μ · √L0 (lead-time jitter dominates here)
safety stock: SS = s − D_L
stockout probability: P(stockout) = 1 − Φ(SS / σ_L)
- Daily consumption — how fast the crew burns the tracked consumable (e.g. potable water, O₂, or CO₂-scrubber sorbent), in kg/day.
- Reorder point (s) — the buffer level, in kg, that triggers the next cargo launch.
- Resupply quantity (Q) — how much a single cargo vehicle delivers.
- Lead-time jitter (σ) — launch-and-transit schedule uncertainty; higher jitter widens the stockout-risk distribution even with the same average lead time.
- Launch resupply now — forces an out-of-cycle order, useful for testing recovery from a low buffer.
Real cargo vehicles (Progress, Cygnus, Dragon) run exactly this loop for the ISS: mission planners size s and Q against measured consumption rates and historical launch-slip variance so the stockout probability stays acceptably small.
This 2D map view lets you drag to pan and scroll (or pinch) to zoom around the orbit, the same way you'd inspect a real mission-ops trajectory plot.