Fix the degraded interval
Synthetic window lasts 20 minutes. Queue starts 40 jobs, arrivals 12/min and processing 8/min constant; buffer limit 100 jobs. No drops or retries occur. After recovery, processing 16/min with arrivals still 12/min. These simplified rates are not actual system measurements.
| Phase | Net jobs/min | Effect |
|---|---|---|
| Degraded | +4 | 40+4t |
| Boundary | At 15 min | 100 jobs |
| Recovered | −4 | Drain to original 40 |
Calculate the net queue rate
- Subtract processing from arrivals
- Project backlog at each time
- Check limit before planning the whole window
The linear projection stops being a valid unlimited-queue model when the buffer limit is crossed; no overflow behaviour is supplied.
When is the limit reached, and what would an unbounded 20-minute projection show?
Show the worked answer
Limit 100 is reached after 15 minutes:(100−40)/4. The unbounded projection is 120 after 20,20 over limit, so the full window is not supported. If 120 were retained in a larger buffer, returning to 40 at net drain 4 would take 20 minutes.
Find the capacity boundary
| Case | Decision | Reason |
|---|---|---|
| 15-minute degraded window | At limit 100 | No headroom remains |
| 20-minute window, limit 100 | Unsupported | Projection exceeds by 20 |
Choose a shorter window, changed admission rate or explicitly larger buffer before acceptance. A recovery drain plan cannot retroactively prevent earlier overflow.