After NTP's selection step leaves five truechimers a few milliseconds apart, how do the cluster and combine steps produce one offset and pick the system peer?

## Where these steps sit An RFC 5905 client mitigates among its servers in three steps in the **system process**. **Selection** has already discarded falsetickers, servers whose correctness intervals lie outside the majority. What remains are truechimers, all plausibly correct, but not equally good: some are noisier, further away, or slightly off from the rest. The **cluster** step (§11.2.2) thins them statistically, and the **combine** step (§11.2.3) turns the survivors into one offset for the clock discipline. Three quantities appear throughout: - **Offset** `theta_p`: the server's current offset from its clock filter. - **Peer jitter** `psi_p`: how much that server's own recent samples scatter. - **Root distance** `lambda`: the maximum error from all causes between the client and the primary reference behind that server. ## Ranking: the merit factor Each survivor gets a merit factor `stratum × MAXDIST + lambda`, with `MAXDIST` equal to 1 s, and the list is sorted by it, lowest first. Because one stratum step is worth a full second of distance, and real root distances are milliseconds, **stratum decides the order** and distance only breaks ties within a stratum. The reference code says it plainly: the metric "is dominated first by stratum and then by root distance". ## Clustering, round by round 1. For each survivor compute its **selection jitter** `psi_s`: the RMS of the differences between its offset and every other survivor's. 2. Find the survivor with the largest `psi_s`, the statistical outlier. 3. Stop if that largest `psi_s` is **smaller than the smallest peer jitter** of any survivor, because the outlier is then within the noise every server already has and discarding it gains nothing. 4. Also stop if only `NMIN` (3) survivors remain. 5. Otherwise discard the outlier and go back to step 1. The final largest selection jitter is kept as the system selection jitter `PSI_s`. ## A worked example Five truechimers, offsets and root distances in milliseconds: | Server | Stratum | Offset | Root distance | Peer jitter | Merit (s) | |---|---|---|---|---|---| | A | 1 | +1.0 | 10 | 0.5 | 1.010 | | D | 2 | +4.6 | 15 | 0.4 | 2.015 | | B | 2 | +1.4 | 20 | 0.5 | 2.020 | | C | 2 | +0.7 | 40 | 0.6 | 2.040 | | E | 3 | +1.2 | 8 | 0.5 | 3.008 | - **Round 1:** D's selection jitter is about 3.53 ms, the largest and above the smallest peer jitter (0.4 ms). D is discarded. - **Round 2:** C's is about 0.53 ms, still above the smallest remaining peer jitter (0.5 ms). C is discarded. - **Round 3:** three survivors remain, equal to `NMIN`, so clustering stops with A, B and E. ## Choosing the system peer The first survivor in merit order, **A**, becomes the system peer. Its variables become the client's system variables: stratum is A's plus one, the reference ID and reference time are A's, and root delay and dispersion build on A's. This is what a downstream client sees when it queries this one. RFC 5905's reference code adds one refinement: if the previous system peer has the same stratum as the new first survivor, it is kept, to avoid **clock hopping** between near-equal servers. ## Combining The combine algorithm weights each survivor's offset by `1 / lambda` and normalises: - weights: A 1/10, B 1/20, E 1/8, which is 0.100, 0.050 and 0.125, summing to 0.275; - weighted offsets: 0.100 × 1.0 + 0.050 × 1.4 + 0.125 × 1.2 = 0.320; - combined offset: 0.320 / 0.275 ≈ **+1.16 ms**. E ranked last but carries the largest weight, about 45%, because its root distance is shortest. Rank chooses whose identity the client inherits; distance decides whose offset counts most. The system jitter is then `PSI = sqrt(PSI_s^2 + PSI_p^2)`, combining the selection jitter with the peer jitter. ## Why not trust only the best server - Averaging several truechimers reduces independent noise that any single server's path adds. - Keeping at least three survivors means losing one does not leave a single unchecked source. - The reference code notes the trade-off: jitter can sometimes be lower without combining, "especially when frequent clockhopping is involved", and lets an operator designate a preferred peer instead.