The Suppression Test and Interval Doubling

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

The Suppression Test and Interval Doubling

A node with redundancy threshold k = 4 hears three consistent DIO messages and no conflicting DODAG information during the current interval. The chapter’s own practitioner check turns that into a scheduled-transmit-time decision: with c = 3 counted against k = 4, is that count enough to suppress the retransmission? This audit asks the question that comparison invites: does c = 3 actually clear the k = 4 threshold, and what does the strict count comparison say the node must do next?

Companion to the chapter Trickle: Timing RPL Messages — every number here comes from that chapter.

Ada: This chapter turns on two numeric rules – suppress when c >= k, and double the interval while things stay consistent. The first I can check on the chapter’s own values; the second is symbolic, so I will mark the illustrative numbers as illustrative.

The suppression decision (the practitioner case, k = 4, c = 3):

• c < k because 3 < 4, so the node transmits its DIO. It would have suppressed only at c >= 4. The test is a strict count comparison, not “close enough.”

Interval doubling (symbolic, with one clearly-illustrative ladder). A Trickle node transmits at most once per interval, and each consistent interval doubles: I, 2I, 4I, and so on, so over a stable window the DIO count grows with log2 of elapsed time rather than linearly. Take an illustrative I_min = 1 s (RFC 6206 leaves the exact value configurable):

• Intervals 1, 2, 4, 8, 16, 32 s sum to 1 + 2 + 4 + 8 + 16 + 32 = 63 s, using only 6 intervals.
• So a stable node sends at most 6 DIOs across roughly 63 s, versus 63 DIOs from a fixed 1 s timer – about a 10x reduction, and the gap widens as the window grows because 6 ~= log2(64).

The audit shows the saving is logarithmic, not a flat suppression rate: doubling is what lets a stable dense mesh fall almost silent, while the strict c >= k test still forces a copy exactly where redundancy is missing.

Every number above is taken from the chapter’s own material and re-derived step by step.