Can an exactly solvable birth-death chain explain why short-lived printer fleets die out?
research/selfrep-extinction
Exact mean extinction time of a wearing-out printer fleet as a birth-death chain (stylised, assumed inputs): explains the die-outs in kind, within about 35% only after a post-hoc fix.
What it found
Follow-up to selfrep-wearout. The fleet is a birth-death chain with an absorbing state at zero, and its mean extinction time is solved exactly and checked against a closed form and Monte Carlo. From one seed machine it grows from 358 h (mean life 100 h) to 3967 h (200 h) to 41,602 h (300 h), but the wear-out simulation dies out 1.8–2.5× sooner. Scaling births by the chance a build outlives its machine brings the two within about 35% for a lone seed (16–18% at 200–300 h), a fit made after seeing the gap; it is 1.7–1.9× too short for four seeds at 300 h. Stylised, with assumed inputs; the 500 h rows are unusable.
A figure from its own output
Paper, code and results
More in Self-replicating manufacturing
- Does paying for spares late rescue the long repair queue of a printer shop?Does paying for spares at service start rescue the long repair queue of a printer shop (stylised, assumed inputs): yes, an unbounded queue then beats never repairing (488 against 458 at one bench) and queue caps stop mattering.
- What happens to a repairing printer shop when repairs need labour?Repair labour as a limit on a repairing printer shop (stylised, assumed inputs): with few repair benches an unbounded queue of broken machines is dead stock and does worse than never repairing; capping the queue recovers most of the gain.
- When is repairing a printer worth more than building a new one?Repair versus replacement in a replicating printer shop (stylised, assumed inputs): repair wins iff its cost share is below its success probability, but only if spares are held back from new builds.
- How much does making its own spare parts cut the cost of repairing a printer?How much making its own spare parts cuts a printer shop's repair cost (stylised, assumed inputs): the printer alone makes none of the wear parts, so in-house spares barely move the fleet; the breakdown rate matters more.
- Does a printer shop lose its printed-bushing gain once a printed spare takes print hours?Does charging printed spares their print hours erase the printed-bushing gain (stylised, assumed inputs): the fleet ignores waits up to ~500 h per repair because it is import-limited, and the gain was within noise anyway.
- Is the lone-printer die-out an early birth-death accident?Exact Markov-chain test of why a lone replicating printer dies out (stylised, assumed inputs): about a fifth die before a fleet forms at 500 h mean life; wear-out lives remove it.
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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.