This is a single-server queue (M/M/1-style): jars ship at a rate driven by "daily order volume", a fraction come back as tickets depending on how far transit heat sits from the calm midpoint, and a single support desk clears one ticket at a time at a fixed service rate. Ticket wait time compared against your SLA target determines the on-time rate — the same pipeline the 3D version renders as a warehouse-to-bins scene, drawn here as a flow diagram plus a live queue-length chart.
issue rate = 0.05 + 0.55 · clamp(|heat-50|/50)
ρ (utilization) = arrival rate / service rate
wait grows sharply as ρ → 1 (queueing theory)
- Warehouse → Transit → Doorstep → Inbox → Desk → Bin — every jar's route through the diagram.
- Desk utilization ρ — ratio of ticket arrival rate to the desk's fixed service rate; above ~85% the queue grows without bound.
- Auto-refund — routes crystallized/wrong-item tickets straight to resolution, skipping the desk and lowering ρ.