$3.(20$ points$)$ Queues

Let us say you are in a line at the grocery store or bank like I was last weekend. One

line, yet there are $3$ clerks$/$tellers which service the same line. Simulate the following,

Clerk $1-$ Services customers on the average $1/$min

Clerk $2-$ Services customers on the average $0\mathrm{.}5/$min

Clerk $3-$ Services customers on the average $0\mathrm{.}75/$min

Customers $-$ Arrive at $4/$minute intervals. When the line gets to $5$ customers add one

more Clerk with the same service rate as Clerk $1.$ Add one more clerk similarly for each

$5$ customers. Take tellers away when they have serviced the line according to how they

were added. For instance, if a $4$th clerk was added to the line because there were $5$

customers waiting then remove the clerk when the customer count in line goes to zero.

What is my average customer wait time? What is the max number of customers in the

line? If you randomize servicing and arrival times by $+-50\%$ how does this change the

results?