How much load can a shared lab instrument carry when its twin assumes exponential service?

research/queue-twin

How much load a shared lab instrument carries when its twin assumes exponential service: exact Pollaczek–Khinchine wait off by (1+c²)/2, twin admits ρ=0.667 vs real 0.444 (c²=4) or 0.133 (c²=25), tails 11.7× worse, infinite mean wait for Pareto index < 2, and a plug-in c² repair that violates the SLA 70–89% of the time.

8 tests

What it found

With Poisson arrivals and one server, the mean wait is exactly ρ(1+c²)/(2(1−ρ)) service times (Pollaczek–Khinchine; matched to a 1.5-million-job simulation within one standard error), so a twin with exponential service is off by (1+c²)/2 at every load. At a mean-wait SLA of 2 service times the twin admits ρ=0.667 while the real instrument admits 0.444 (c²=4) or 0.133 (c²=25): real mean waits 2.5× to 13× the SLA, and 11.7× the twin’s tail-exceedance claim at c²=4. With a Pareto tail of index below 2 the real mean wait is infinite. A negative repair result: a plug-in c² fitted from n logged service times violates the SLA in 70–89% of repeats for n=25–1600, and a 90% bootstrap bound still 46% at n=1600. Stylised (Poisson arrivals, one server, simulated “real” instrument).

A figure from its own output

Figure produced by research/queue-twin: admitted_load — queue-twin/experiments/admitted_load.svg, written by the project's own experiment code.

Paper, code and results

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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.