A heartbeat twin that drops packets independently: how often does the real bursty link trip a missed-beat watchdog, and what timeout is safe?

What it found

At 5% mean loss a watchdog that e-stops after m = 5 missed heartbeats false-trips once in 3.4×10⁶ ticks (18.7 h at 50 Hz) in the i.i.d.-loss twin but every 235–990 ticks (5–20 s) on a two-state bursty link with mean burst 2–50, from an exact recursion checked against enumeration and Monte Carlo. The error is not monotone in burst length: it is worst at L ≈ m, where the mean time to trip is only ≈ em/p. For a 10⁶-tick target the twin picks m = 5 (0.10 s to detect a dead link) while the real link needs 16–154 (0.3–3.1 s) growing linearly in L, and with L unknown no affordable timeout guarantees it. Stylised: Gilbert channel, plain miss counter, no link traces.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.