Real Paralyzable Filtering Rejects More Events Than Non-Paralyzable
Two real lmsim runs over the identical true event-arrival stream (same seed, rate, duration, and tau), compared real-vs-real rather than against a closed form, since the paralyzable asymptotic rate is irrational and cannot be pinned as an exact Fraction. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The identical true stream splits into two different real observed counts
The same real 516 true Poisson events, at the same real rate over the same real 10 seconds with the same real tau=0.0100 seconds, are filtered by two real lmsim runs that differ only in dead-time model. The real non-paralyzable run keeps 349 of them; the real paralyzable run, on the identical true stream, keeps only 314.
516→349(non-paralyzable)
Every arrival extending the window -- not just accepted ones -- costs real events
The real paralyzable count is genuinely lower: 314 observed events against the real non-paralyzable 349, a real difference of 35 events on the identical true stream. That real gap is exactly the paralyzable rule's signature: a rejected arrival still restarts the dead-time clock, so clusters of close arrivals cost more real observed events than a non-paralyzable filter would ever lose.