Vehicles arrive at a stop sign with an average rate of 200 vph (vehicles per hour). It is estimated that the average departure rate from this stop sign is 250 vph. (a) Assume both the arrival and departure processes are Poisson. Compute [3 points] i. the average waiting time in queue, ii. the average time spent in the system, iii. and the average queue length at this stop sign. (b) Suppose that the stop sign was converted into a yield sign and the average departure rate stays the same, but the departure is now uniform. Compute [3 points] i. the average waiting time in queue, ii. the average time spent in the system, iii. and the average queue length at this stop sign. (c) In order to further reduce the wait time, a traffic light was installed to replace the yield sign. Assume the departure process after the light was installed remained uniform (deterministic). It was found that the average waiting time in the queue after the traffic light was installed was 8 sec/veh. What is the average departure rate (in vph) from the traffic light if the average arrival rate remains the same