Beacon Timing and Reserved Airtime

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

ADA · CALCULATION AUDIT

Beacon Timing and Reserved Airtime

Twelve shelf sensors report by contention while two safety sensors must land one status frame inside a 100 ms control window, so the coordinator reserves a Guaranteed Time Slot for each. At BO = 6, SO = 3 every slot is 7.68 ms, so three one-slot reservations consume 23.04 ms — 18.75% of the active superframe — yet the beacon interval itself stays at 983.04 ms. This audit re-derives that schedule and asks whether reserving a GTS actually meets the deadline, or only protects airtime while the roughly one-second beacon interval never gets shorter.

Companion to the chapter 802.15.4 Collisions and Scheduling — every number here comes from that chapter.

Ada: The beacon schedule is not just a MAC feature; it is a clock budget. Keep the symbol arithmetic visible before accepting a low-power or bounded-latency claim.

• Base superframe: 960 symbols * 16 us/symbol = 15360 us = 15.36 ms.
• Low-duty cycle, BO = 6, SO = 0: BI = 960 * 2^6 = 61440 symbols; 61440 * 16 us = 983040 us = 983.04 ms; SD = 960 symbols = 15.36 ms; active fraction 15.36 / 983.04 = 0.015625 = 1.5625%; inactive time 983.04 - 15.36 = 967.68 ms.
• Slot-sizing case, BO = 6, SO = 3: SD = 960 * 2^3 = 7680 symbols; 7680 * 16 us = 122.88 ms; slot time 122.88 / 16 = 7.68 ms.
• Three one-slot GTS reservations consume 3 * 7.68 = 23.04 ms, which is 3 / 16 = 18.75% of the active superframe and leaves 122.88 - 23.04 = 99.84 ms for the rest of the active-period work.

The physics check is the conclusion: a one-second beacon interval can be excellent for sleeping nodes, but it cannot satisfy a 50 ms control deadline unless the schedule changes. A GTS protects airtime; it does not make the beacon interval shorter.

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