What the 10x Deadband Number Really Depends On

What the 10x Deadband Number Really Depends On

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

foundations
math-foundations
calculation-audit
edge-fog
Ada ADA · CALCULATION AUDIT

What the 10x Deadband Number Really Depends On

The chapter reports a 10x reduction from edge deadbanding: 100 sensors at 200 bytes each produce 20 KB/s, and suppressing 90% leaves 2 KB/s. But the reduction factor is 1 / (1 - s), so a ten-point swing in the suppressed fraction moves the headline from 5x to 100x. This audit reproduces the number and shows what the 10x deadband number really depends on.

Companion to the chapter Lab: Edge-Fog Computing — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is suppressed messages. The middle card applies the page rule. The green card is traffic reduction. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

Suppressed messages changes traffic reduction An input card leads through the rule reduction = 1 / (1 - suppressed fraction) to the traffic reduction result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. The headline ratio is very sensitive to how often the real signal stays inside the deadband.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 90 %.

  2. 2

    Name the relationship. reduction = 1 / (1 - suppressed fraction)

  3. 3

    Substitute with units. 1 / (1 - 0.90) = 10.00 times

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change suppressed messages

Try Predict the direction of reduction = 1 / (1 - suppressed fraction). Test another suppressed messages, then compare traffic reduction.

90 %
Chapter baseline
Traffic reduction

Observe The headline ratio is very sensitive to how often the real signal stays inside the deadband. Reset suppressed messages to 90 and compare traffic reduction.

Explain The headline ratio is very sensitive to how often the real signal stays inside the deadband.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only suppressed messages moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only suppressed messages. It is not a field prediction.

TryThe chapter reports a 10x reduction from edge deadbanding: 100 sensors at 200 bytes each produce 20 KB/s , and suppressing 90% leaves 2 KB/s . Use Check derivation.
ObserveThe displayed ledger resolves 10x, 100, 200 bytes, 20 KB/s, 90% at full precision. This audit reproduces the number and shows what the 10x deadband number really depends on. Check derivation shows this.
ExplainThe design meaning is why the chapter demands stress and tail measurement rather than a quiet-minute average: the deadband ratio is hypersensitive to the one assumption nobody measures — how often the signal truly holds still — so an honest lab reports the suppression fraction it observed under load, not a single round multiplier. Check derivation confirms it.

Ada: The section reports a “10x reduction” from edge deadbanding and then, to its credit, insists the number “is only trustworthy if it survives scrutiny.” Let me reproduce it and then show exactly how fragile that headline is.

The raw stream first:

  • 100 sensors x 1 msg/s x 200 bytes = 20,000 bytes/s = 20 KB/s
  • Suppress 90%, so 10% survives: 20,000 x 0.10 = 2,000 bytes/s = 2 KB/s
  • Reduction: 20,000 / 2,000 = 10x

The arithmetic holds. But the reduction factor is 1 / (1 - s) for a suppressed fraction s, and that curve bends sharply:

  • s = 0.80 gives 1 / 0.20 = 5x
  • s = 0.90 gives 1 / 0.10 = 10x
  • s = 0.95 gives 1 / 0.05 = 20x
  • s = 0.99 gives 1 / 0.01 = 100x

A ten-point swing in the suppression fraction moves the headline from 5x to 100x. And this is only the mean: if a burst suppresses nothing, the peak upstream rate snaps back to the full 20 KB/s regardless of the 10x average — and the peak is the capacity a link must actually be provisioned for.

The design meaning is why the chapter demands stress and tail measurement rather than a quiet-minute average: the deadband ratio is hypersensitive to the one assumption nobody measures — how often the signal truly holds still — so an honest lab reports the suppression fraction it observed under load, not a single round multiplier.

Technical boundaries
The deadband ratio deliberately does not simulate the signal's value distribution, correlated bursts, sensor noise, anomaly loss, or queueing; it assumes a fixed suppression fraction applied uniformly to the raw message rate.

Work the audit first, then check the displayed derivation.

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