Problem $3(20\%)$

A bank branch has two office employees who are equally efficient and capable of attending $60$

operations$/$hour on average, with the true time distributed exponentially. Customers arrive at the bank

branch following a Poisson process with a mean rate of $100$ customers$/$hour$.$ Determine the followings

$($show your results in minutes$)$:

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

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

$($iii$)$ Find the service mean service rate $.(2)$

$($iv$)$ Solve the queuing problem using formulas and simulation to complete the following table $(10).$

Simulate for $10,000$ customers.

$($v$)$ At any time, find the probability of having $3$ customers in the bank branch. $(4)$