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:

$1.$ Average number of vehicles waiting in the queue, Lq

$2.$ Average waiting time in the queue, Wq

$3.$ Average time in the system, W$.$

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

$1.$ Utilization ratio, $\backslash$rho $=\backslash$lambda $($arrivals for the entire system$)/\backslash$mu $($service rate per server$).$

$2.$ Replace L with Lq In the equations for W and Wq $.$

$3.$ Average number of units in the system, L $=$ Lq $+\backslash$rho