Why the Parent Comparison Is a True Tie
Why the Parent Comparison Is a True Tie
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
Why the Parent Comparison Is a True Tie
Router F2-A hears two candidate parents: F3-A advertises Rank 256 with a local link increase of 256, while F3-B advertises Rank 384 with a smaller increase of 128. Both routes land on exactly Rank 512, and the lab warns that a tie like this must not be broken by picking the parent with the smaller advertised number. This audit asks the question that warning invites: is the 512-512 tie a genuine cancellation between advertised Rank and link cost, or just an accident that would break under a small nudge?
Companion to the chapter Lab: Designing an RPL Network — every number here comes from that chapter.
See the relationship before changing it
The figure reads from left to right. The blue card is f3-a local increase. The middle card applies this page's rule. The green card is resulting rank. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only f3-a local increase, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 256 rank.
- 2
Name the relationship. resulting rank = advertised rank 256 + local increase
- 3
Substitute with units. 256 + 256 = 512 rank
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change f3-a local increase
Try Predict the direction of resulting rank = advertised rank 256 + local increase. Test another f3-a local increase, then compare resulting rank.
Observe Only the resulting sum exposes whether two candidate parents truly tie. Reset f3-a local increase to 256 and compare resulting rank.
Explain Only the resulting sum exposes whether two candidate parents truly tie.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Compare parent F3-A as 256 + 256 with F3-B as 384 + 128, then choose Check audit.
The two written calculations both produce 512; nudging F3-A's local increase to 257 breaks the state to 513 versus 512.
A 128-point advertised-Rank advantage cancels a 128-point local-link penalty, so only resulting Rank exposes the genuine tie.
Ada: The lab hands you two candidate parents and reports a tie. A tie is easy to state and easy to under-read, so let me check that it is a real tie and not a rounding accident, and then show what the tie is actually made of.
Router F2-A hears two parents, and candidate Rank is advertised Rank plus the local increase:
- Via F3-A:
256 + 256 = 512 - Via F3-B:
384 + 128 = 512
Both land on exactly 512, so the tie is exact. But it is not a coincidence, it is a cancellation. F3-A advertises the lower Rank (256 versus 384, an advantage of 384 - 256 = 128) yet charges the higher local increase (256 versus 128, a penalty of 256 - 128 = 128). The two 128s cancel:
- Advertised-Rank advantage of F3-A:
128 - Local-increase penalty of F3-A:
128 - Net:
128 - 128 = 0
The lesson is narrow but load-bearing: advertised Rank is not the decision variable, resulting Rank is, and here the parent that looks “closer to the root” buys no real advantage once its costlier link is counted. The tie is also fragile: nudge either local increase by a single unit (256 -> 257 gives 256 + 257 = 513) and F3-B wins by one. That is exactly why the lab tells you to record concrete tie-break evidence, such as stability, hysteresis, or link history, instead of preferring the parent with the smaller advertised number.
Every number above is taken from the chapter’s own material and re-derived step by step.
Technical boundaries: The two-parent comparison omits MRHOF hysteresis, ETX sampling noise, parent stability history, congestion, energy state, and the downstream cost of a parent switch.