Consider the following single$-$server queue: the inter$-$arrival time is exponentially distributed with a mean

of $10$ minutes, and the service time has a triangular distribution with a maximum of $12$ minutes, a minimum

of $6$ minutes, and a mode of $9.$ Do the following $($show your results in minutes$)$:

$($i$)$ Write the queuing system using Kendall notation. $(2)$

$($ii$)$ Find the mean arrival rate $(2)$

$($iii$)$ Find the mean service time and variance of service time ${}^2($Hints: $=\frac{a+b+c}{3}$ and ${}^2=$

$\frac{a^2+b^2+c^2-ab-ac-bc}{18}(4)$

$($iv$)$ Solve the queuing problem using formulas and simulation to complete the table. Simulate

for $1,000$ entities. $(12)$