Abstract
A one-lane road briefly expands to two lanes at a stoplight before merging back into one. Some 10 drivers always choose the right lane, while others pick the shorter lane, favoring the right in a tie. In our 11 previous paper, we represented arrival sequences as binary strings that created lattice paths, and analyzed how 12 many vehicles end up in the left lane, drawing heavily on connections to ballot paths. Presently, we consider 13 limited lane capacities: when the right lane fills, a gap can form in the left lane. We calculate the expected size 14 of this gap based on the proportion of each driver type, including new bijections. 15