30-station line, live discrete-event run, bottlenecks and queues.
The science
The line is a series of 30 stations with finite buffers. Parts arrive with exponential inter-arrival times (mean 1/lambda); each station needs a cycle time (jittered 0.85 to 1.15), can break down (exponential time to failure MTBF, repair MTTR) and blocks the station before it when the next buffer is full. This is a discrete-event simulation: a priority queue of timed events (arrival, finish, failure, repair), the same engine as the 3D page.
Bottleneck. A station with c parallel servers and batch b can pass at most c b / T_cycle units per second; the whole line can never beat the slowest one. Throughput is then min(lambda, capacity x availability). Availability of a station is MTBF / (MTBF + MTTR).
Queues. For a single station with Poisson arrivals and exponential service the Erlang C formula gives the probability of waiting C(c, a) and the mean time in system W = C / (c mu - lambda) + 1/mu. Little's law says L = lambda W for any stable system. The checks below run the in-page event simulation on M/M/c queues and compare with these exact results, and apply Little's law to the plant run itself (average work in progress = accepted rate x mean flow time).
Honest simplifications: data are illustrative design numbers, not measured production figures; service is near-deterministic (not exponential) in the plant, so the Erlang results apply only to the dedicated check cases; transport time is a fixed delay; no operators, shift breaks or learning effects.