The Break-Even Millijoules

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

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.

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.

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