Does paying for spares late rescue the long repair queue of a printer shop?
research/selfrep-repairpay
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 it found
Follow-up to selfrep-repairlabour. That project found an unbounded repair queue is dead stock (414 working machines against 458 for never repairing, one bench, B = 40) when spares are bought at breakdown. Buying them when a bench frees up instead reverses it: 488 against 458, and 572 against 504 with four benches. The queue is as long (about 3400 machines) but ties up no vitamins, and capping it no longer helps (caps of 1–200 all give 484–492 at one bench; no standard errors computed, so no optimum cap is claimed). Stylised: assumed inputs, first-come service, a machine unaffordable at its turn is retired.
A figure from its own output
Paper, code and results
More in Self-replicating manufacturing
- 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.
- Can a quasi-stationary approximation predict how long a small printer fleet lasts?Quasi-stationary approximation of how long a small replicating-printer fleet lasts (stylised, assumed inputs): within 5% of the exact mean time once a correction for early die-out is applied, poor for the shortest lives.
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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.