Problem $2$: $(15)$

Given: The average arrival rate at a given bridge toll plaza is $20$ vehicles per minute. There are

three toll booths, and the average service time at each booth is $8$ seconds. Analyze the system as

a FIFO M$/$M$/3$ queuing discipline.

Find:

Average number of vehicles waiting in the queue, $L_a$

Average waiting time in the queue, $W_a$

Average time in the system, W$.$

Please note the following corrections to Table $18\mathrm{.}1$ equations in the textbook regarding FIFO

$\frac{M}{M}\frac{?}{N}$ systems:

Replace $L$ with $L_Q$ In the equations for $W$ and $W_9.$

Average number of units in the system, $L=L_Q+$