The same real lmsim run's aggregate event counts, compared against the closed-form non-paralyzable asymptotic rate -- close, not identical, as finite-sample statistics predicts. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A real dead-time filter genuinely thins the true event count

A real lmsim run simulates 516 true Poisson events at a real rate of 50 per second over 10 seconds, then applies a real non-paralyzable dead-time filter with tau=0.0100 seconds. Only 349 of the real true events survive as observed.

516349516\to349
Real event-arrival rate vs. closed-form asymptoteReal true and observed event counts from one lmsim run, compared against the closed-form non-paralyzable prediction.true=516 eventsobserved=349 eventsmeasured=34.9000 Hzasymptotic=33.3333 Hz

The real measured rate lands close to the closed-form asymptote

The real observed count divides the real 10-second window into a real measured rate of 34.9000 hertz. The closed-form asymptotic prediction, true rate over one plus true rate times tau, is 33.3333 hertz — the real finite-sample run lands within a real 4.7000 percent of that closed form, close but not identical, as finite-sample Poisson noise predicts.

34.900033.333334.9000\approx33.3333
Real event-arrival rate vs. closed-form asymptoteReal true and observed event counts from one lmsim run, compared against the closed-form non-paralyzable prediction.true=516 eventsobserved=349 eventsmeasured=34.9000 Hzasymptotic=33.3333 Hz