Homework Assignment $8$:

$1.$ The outside arrival rate refers to the rate of parts entering the repair station for the very first

time. The overall arrival rate refers to the rate of all parts entering the repair station.

a$)$ For the current system, determine the maximum outside arrival rate that makes the

bottleneck station$$s utilization equal one.

b$)$ For the proposed system, determine the maximum outside arrival rate makes the

bottleneck station$$s utilization equal one.

Hint: the bottleneck station is the one with the highest utilization.

$2.$ Readjusting the arrival rates and number of servers.

a$)$ For both the current and proposed systems, set the outside arrival rate to the minimum of

the two maximum outside arrival rates you determined in Question $1$a$)$ and Question $1$b$).$

b$)$ For both the current and proposed systems, add a server to the bottleneck station $($so it is

now M$/$M$/2).$

c$)$ Re$-$compute the results and compare the two system designs.

Hint: $$lambda$$ in Queueing Tools refers to the overall arrival rate