The PSM/eDRX Timer Ledger

The PSM/eDRX Timer Ledger

Ada audits the PSM/eDRX timer ledger — one time conversion, two measured-energy equations

ADA · CALCULATION AUDIT

Foundations · optional mathematics and physics

The PSM/eDRX Timer Ledger

One time conversion, two measured-energy equations, ~4 minutes

A water meter that reports once a day spends almost all of its 86,400-second cycle asleep, waking only for a short post-uplink window to catch queued settings — and a maintenance campaign adds a temporary window where it listens more often before returning to that low-power policy. The chapter is deliberate that this is not a battery-life button: requested PSM and eDRX timers are only proposals until the network grant and a measured current trace confirm them. So this audit rebuilds the timer ledger to ask what it can honestly claim — the structure of the lifetime calculation, or the lifetime itself?

Companion to the chapter NB-IoT Power Saving (PSM/eDRX) — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is granted reachable time. The middle card applies this page's rule. The green card is unreachable psm time. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only granted reachable time, so the numeric fixture does not switch without explanation.

Walk the arrows. More network-granted reachable time leaves fewer seconds in unreachable power-saving mode.

Derive the baseline in four named moves

1. 1

   Name the input. The chapter baseline is 3600 s/day.

2. 2

   Name the relationship. unreachable time = 86,400 s/day - reachable time

3. 3

   Substitute with units. 86,400 - 3,600 = 82,800 s/day

4. 4

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

Predict, then change granted reachable time

Try Predict the direction of unreachable time = 86,400 s/day - reachable time. Test another granted reachable time, then compare unreachable psm time.

Granted reachable time

3600 s/day

Chapter baseline

Unreachable PSM time

Observe More network-granted reachable time leaves fewer seconds in unreachable power-saving mode. Reset granted reachable time to 3600 and compare unreachable psm time.

Explain More network-granted reachable time leaves fewer seconds in unreachable power-saving mode.

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

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

TryRun Calculate with the chapter's active, eDRX, and PSM currents plus their stated dwell times.

ObserveReachable and unreachable seconds must sum to the 86,400-second daily cycle before the average-current or lifetime structure is valid.

ExplainEach state's charge is measured current times dwell seconds divided by 3,600; a brief high-current attach can therefore dominate the daily PSM ledger.

Ready: use the stated baseline inputs, then compare each displayed result.

Convert the daily cycle

The normal meter example reports once per day, so the cycle length is fixed before any modem grant is inserted.

daily_cycle_seconds = 24 h x 60 min/h x 60 s/min = 86400 s

normal_reachable_seconds = granted_active_timer_s + granted_eDRX_paging_seconds

normal_unreachable_seconds = 86400 - normal_reachable_seconds

For PSM-only normal operation, the eDRX paging term is zero rather than guessed.

Keep current as measured physics

Every current claim stays tied to a measured state and duration.

state_mAh = measured_current_mA x measured_duration_s / 3600

normal_day_mAh = sleep_mAh + wake_send_mAh + active_timer_mAh + paging_mAh + retry_mAh + host_overhead_mAh

maintenance_day_mAh = normal_day_mAh + maintenance_eDRX_mAh + command_transfer_mAh + exit_validation_mAh

The monthly maintenance example changes the mode ledger; it does not license a battery-life claim without a return-to-PSM trace.

This audit proves the calculation structure only. Because the chapter has no measured current table, the release gate must still demand real trace values before claiming lifetime.

Every symbol above is taken from the chapter's own PSM/eDRX timer example and re-derived step by step.

Technical boundaries. Coverage repetitions, network timers, temperature, cell reselection, battery pulse limits, self-discharge, and ageing are omitted from this periodic state model.