Consider the intersection of two one way streets, both with a single lane, with a mainline road

and a minor road. This minor road is controlled by a yield sign. The first driver on the minor

street will wait for a critical gap of $7sec$ on the mainline before proceeding. If the first vehicle

accepts a gap, the following driver will take $2sec$ to move up and then make the same

assessment for the critical gap to go$/$no$-$go $($so if a gap were $8sec,$ the first vehicle accepts, the

second vehicle moves up only sees a $6$ sec gap and does not go$,$ rejecting the $6$ sec gap$).$ Assume

an infinite queue on the minor road approach.

a$)$ Assuming a mainline vehicle just passed at $t=0,$ calculate how many minor street vehicles are

able to cross in the first minute given the following mainline arrival times

b$)$ Could it be worse? If so$,$ prove it by deriving your worst case set of arrival times for the same

quantity of vehicles from a$.$

c$)$ Could it be better? If so$,$ prove it by deriving your best case set of arrival times for the same

quantity of vehicles from a $($assume minimum headway on the mainline is $2s).$