Queueing theory · M/M/c · four doors

THE LAST TEN PERCENT COSTS EVERYTHING

L = λW · Wq = C(c, ρ)(1 − ρ)

Little's Law says the number of trucks in your yard is simply the arrival rate times how long each one stays — always, for any queue, no assumptions. The second line is the one that bites: waiting time carries (1 − ρ) in the denominator, so as the doors approach full utilisation the wait does not rise, it goes vertical. At 85% booked the average truck waits half an hour. At 95% it waits two hours. Nothing about the dock changed.