Problem $2$

A toll booth on a turnpike is open from $8$:$00$ A$.$M$.$ to $12$ midnight. Vehicles start arriving at $7$:$45$ A$.$M$.$ at a uniform deterministic rate of six per minute until $8$:$15$ A$.$M$.$ and from then on at two per minute. If vehicles are processed at a uniform deterministic rate of six per minute, determine when the queue will dissipate, the total delay, the maximum queue length $($in vehicles$),$ and the longest vehicle delay under FIFO.