Given: Vehicles arrive at a single toll booth opening at $9$:$00$ A$.$M$.,$ at which time vehicles begin to arrive at a rate of $360$ veh$/$hr$.$ After $45$ minutes, the arrival flow rate declines to $150$ veh$/$hr$,$ and it continues at that level until $3$:$30$ P$.$M$.$ If the time required to distribute the brochure is $15$ seconds, and assuming D$/$D$/1$ queuing and FIFO. Find: a$)$ Draw the queuing diagram. $(15$ points$)$ b$)$ When does the initial queue clear. $(10$ points$)$ c$)$ The total delay. $(8$ points$)$ d$)$ The longest queue length $($in vehicles$).(6$ points$)$ e$)$ The longest delay. $(8$ points$)$ f$)$ The wait time for the $300$ th vehicle to arrive. $(8$ points$)$ Hint: Please use the graphic method to solve this problem.