Problem $1$: Vehicles begin to arrive at a toll booth at six vehicles per minute starting from $9$ A$.$M$.$

The booth opens at $9$:$15$ A$.$M$.$ and services at a rate of seven vehicles per minute until $9$:$45$ A$.$M$.$

From $9$:$45$ A$.$M$.$ up to queue clearance time, the service rate is $10$ vehicles per minute. Assuming

$\frac{D}{D}\frac{?}{1},$ determine:

a$.$ the queue clearance time

b$.$ the total vehicle delay

c$.$ the average delay per vehicle

d$.$ the time at which the longest queue occurs

e$.$ the longest queue $($maximum queue length$)$

f$.$ the longest vehicle delay under FIFO

g$.$ the longest vehicle delay under LIFO