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.
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.