The Burst-Capacity Ledger: Bytes, Rates, Airtime, and Retry Load

Ada carries the chapter’s device ledger through overhead, outage timing, raw airtime, and retry load

ADA · CALCULATION AUDIT

The Burst-Capacity Ledger: Bytes, Rates, Airtime, and Retry Load

Three hundred devices each sending a 40-byte reading every 5 minutes offer a payload average of just 320 bps — small enough to look like the shared channel has room to spare. But framing and acknowledgements push the real exchange near 100 bytes, and if those same 300 devices reconnect inside a 15-second recovery window the offered load spikes to 16,000 bps, whose raw airtime alone occupies nearly one second on a 250 kbps PHY. This audit carries the ledger past the payload average — through overhead, outage timing, and retries — to ask whether the channel really has usable headroom.

Companion to the chapter Bandwidth and Channel Capacity — every number here comes from that chapter.

The ledger, line by line

Check	Inputs from this chapter	Arithmetic	Result
Payload average	300 devices, 40 B, 5 min = 300 s	300 x 40 x 8 / 300	320 bps
Exchange average	300 devices, 100 B exchange, 300 s	300 x 100 x 8 / 300	800 bps before retries
Outage burst	300 devices, 100 B exchange, 15 s	300 x 100 x 8 / 15	16,000 bps
Raw burst airtime	300 exchanges, 800 bits each, 250,000 bps PHY	(300 x 800) / 250,000	0.96 s of raw data time
Retry stress	100 devices, 100 B frame, 250,000 bps PHY, 20% retries	100 x 800 / 250,000 x 1.20	0.384 s of raw data time

The rounding happens at the end: 0.96 s is already close to the "nearly one second" warning, and the 0.384 s retry case excludes acknowledgement, backoff, and carrier-sense time. Those omitted terms are why a clean record still needs a busy-window proof.

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