Fix the dispatch boundary rule
Synthetic batch sends at minute 10 and 20. An event arriving exactly at a boundary is included in that send. Events arrive at minutes 1,8,10,11; local condition requires each wait≤8 minutes. These elapsed minutes share one zero point.
| Arrival minute | Dispatch minute | Wait min |
|---|---|---|
| 1 | 10 | 9 |
| 8 | 10 | 2 |
| 10 | 10 | 0 |
| 11 | 20 | 9 |
Assign every event to a batch
- Assign the next inclusive boundary
- Subtract arrival from send
- Compare every wait with eight
A favourable average cannot waive an individual maximum condition.
Does batching pass, and how many events breach?
Show the worked answer
No; two events wait nine minutes and breach. Mean wait is(9+2+0+9)/4=5 minutes, but maximum is 9.
Check the maximum delay
| Case | Decision | Reason |
|---|---|---|
| Average 5≤8 | Not sufficient | Policy applies individually |
| Event exactly minute 10 | Wait 0 | Boundary included |
A revised batching rule must reduce both nine-minute waits while retaining its exact-boundary definition. Verify case-level delays, not only batch count.