A2. Let delayed consequences change the next choice
Three service workers each supply one unit of capacity per interval. The domain owner permits two update alternatives: restart all workers in one interval, or one worker per interval over three intervals. It supplies a maximum backlog of two units, a later clearing period and a preference for earlier completion when the limit is met.
MMP.8.SD constructs observation/action order, remaining update work and the transition q_next = max(0, q + demand - active_capacity). Demand is observed before choosing; a later observation can change a later choice. This teaching model assumes constant demand for the displayed comparison and starts with zero backlog.
| Observed demand per interval | All-at-once capacity over three intervals | Rolling capacity | Modeled peak backlog: all / rolling | Supported choice under the supplied criterion |
|---|---|---|---|---|
| 1 | 0, 3, 3 | 2, 2, 2 | 1 / 0 | Both satisfy the limit; the shorter all-at-once update can be chosen. |
| 2.5 | 0, 3, 3 | 2, 2, 2 | 2.5 / 1.5 | All-at-once exceeds two; rolling remains a candidate, with its later clearing obligation. |
At demand 2.5, rolling leaves backlog 1.5 after its third interval. Restored capacity three clears 0.5 per interval, so the supplied clearing period must accommodate three further intervals under these assumptions. The update’s completion and backlog clearance are different results.
The exact recurrence is the simpler calculation. If a fitted or LLM-generated surrogate replaces it, MMP.17 and CMP.7 must supply its target, construction and consequential error. A separately justified peak-response error at most 0.2 relative to this model still rejects 2.5 and admits 1.5. An interval crossing two leaves that constrained choice unresolved: return to the exact recurrence, obtain a relevant observation, take an independently supported narrower action, or stop.
Agreement with the model does not establish agreement with the service. SYSE.10 bounds that reliance; SYSE.47 binds current conditions and the error return; C.24 plans the selected action and SYSE.42 performs it. If an actual restart reveals another service rate, return through MMP.14 to the affected observation and transition. Do not relabel the earlier forecast as an observed effect.