The Break-Even Millijoules

The Break-Even Millijoules

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

The Break-Even Millijoules

The chapter’s ledger says local inference costs about 6 mJ while offloading costs about 2.7 mJ — a 2.2x saving — until a tenfold payload pushes the transmit cost to 24.3 mJ, now 4.1x more than staying local. Energy is just power times time. This audit confirms each figure to find the break-even millijoules where the inequality flips.

Companion to the chapter Fog Energy-Latency Tradeoffs — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is transmit time. The middle card applies the page rule. The green card is offload energy. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

Transmit time changes offload energy An input card leads through the rule energy = (120 mW x transmit ms + 60 mW x 5 ms) / 1000 to the offload energy result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Payload size stretches transmit time until offloading costs more than local work.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 20 ms.

  2. 2

    Name the relationship. energy = (120 mW x transmit ms + 60 mW x 5 ms) / 1000

  3. 3

    Substitute with units. (120 x 20 + 60 x 5) / 1000 = 2.70 mJ

  4. 4

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

Predict, then change transmit time

Try Predict the direction of energy = (120 mW x transmit ms + 60 mW x 5 ms) / 1000. Test another transmit time, then compare offload energy.

20 ms
Chapter baseline
Offload energy

Observe Payload size stretches transmit time until offloading costs more than local work. Reset transmit time to 20 and compare offload energy.

Explain Payload size stretches transmit time until offloading costs more than local work.

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 transmit time moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only transmit time. It is not a field prediction.

TryThe chapter’s ledger says local inference costs about 6 mJ while offloading costs about 2.7 mJ — a 2.2x saving — until a tenfold payload pushes the transmit cost to 24.3 mJ , now 4.1x more than staying local. Use Check derivation.
ObserveThe displayed ledger resolves 6 mJ, 2.7 mJ, 2.2x, 24.3 mJ, 4.1x at full precision. This audit confirms each figure to find the break-even millijoules where the inequality flips. Check derivation shows this.
ExplainTransmit energy scales with payload airtime, so the 2.7 mJ offload path beats 6 mJ locally at the base payload but rises to 24.3 mJ at ten times the data, reversing the placement inequality. Check derivation confirms it.

Ada: The ledger above says local inference costs about 6 mJ, the radio side about 2.7 mJ, and that a tenfold payload can erase the saving. Energy is just power times time, so let me confirm each figure with 1 mW x 1 ms = 1 microjoule.

  • Local. 40 mW x 150 ms = 6,000 uJ = 6.0 mJ.
  • Offload. Transmit 120 mW x 20 ms = 2,400 uJ plus receive 60 mW x 5 ms = 300 uJ, totalling 2,700 uJ = 2.7 mJ — about 6.0 / 2.7 = 2.2x cheaper than local, before overhead.
  • Tenfold payload. Transmit time scales with data size, so 20 ms x 10 = 200 ms and transmit energy becomes 120 mW x 200 ms = 24,000 uJ. With the same receive term that is 24,000 + 300 = 24,300 uJ = 24.3 mJ, now 24.3 / 6.0 = 4.1x more than staying local.

The inequality flips between 2.2x for and 4.1x against as the payload grows, which is why break-even is a measurement, not a rule. And even in the 2.7 mJ case where offload wins on joules, the round trip and fog queue still have to clear the response budget before the energy saving is allowed to count.

Technical boundaries
The energy break-even deliberately does not simulate radio ramp states, payload framing, retransmissions, codec cost, thermal throttling, or latency tails; it multiplies the stated constant powers by durations for one transaction.

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.