Real Dead-Time Filter Ledger

Real Dead-Time Window Rejects, Then Accepts, Genuine Events

Every value in this lesson is rounded to four decimal places from a real lmsim Poisson event-arrival simulation (scenario gen-arrivals, case-studies/poisson-process-dead-time-filter/specs/nonparalyzable_e001.json), not derived from a closed form. 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 window genuinely drops the next arrival

A real lmsim event-arrival simulation records a real true event at t=0.0051 seconds and opens a real 0.0100-second dead-time window. The very next real arrival, at t=0.0106, falls only 0.0055 seconds later — inside the real window — and the real simulation marks it not observed.

1: Δt=0.0055<τ=0.0100⇒dropped1\text{:}\ \Delta t=0.0055<\tau=0.0100\Rightarrow \text{dropped}
Real dead-time window: rejectionThe real dead-time bar opens at the real recorded event; the real next arrival lands inside it and is dropped.tau=0.0100 se0 kept t=0.0051 se1 dropped t=0.0106 s

The real window clears and the next genuine event is kept

A later real arrival, at t=0.0392, lands 0.0341 seconds after the same recorded event — past the real 0.0100-second window — and the real simulation marks it observed, exactly as the non-paralyzable rule requires.

2: Δt=0.0341≥τ=0.0100⇒kept2\text{:}\ \Delta t=0.0341\ge\tau=0.0100\Rightarrow \text{kept}
Real dead-time window: acceptanceThe same real window; the real later arrival clears it and is kept.tau=0.0100 se0 kept t=0.0051 se1 dropped t=0.0106 se2 kept t=0.0392 s