Assume that a maintenance team performs different maintenance operations on the machines of a certain

factory. The time between failures was found to follow an exponential distribution with an average of $2\mathrm{.}5$ hours,

while the time to repair a machine was found to be exponentially distributed with an average of $2$ hours. The

maintenance manager found that the average number of machines waiting in the queue is $3\mathrm{.}2$ machines, with an

average waiting time of $8$ hours. If he wishes to reduce both numbers by hiring another team, he has two options:

$[1]$ to have both teams sharing the same queue, and $[2]$ to have each team with a separate queue. It is required

to:

i$)$ Calculate the average number of machines waiting in queue, for both options,

ii$)$ Calculate the average waiting time in queue, for both cases,

iii$)$ Comment on the comparison, whether they are different or same.