A ticket counter expects customers to arrive at an average rate of $40$ customers$/$hr$.$ There are two service executives who can man the counter, but only one of them mans the counter at a time. The first executive can serve $60$ customers in an hour on average, and the second, $80$ customers in an hour. What would be the difference in the following characteristics of the queue when the two executives are manning the counter independently?

$($Hint: Calculate the values below separately for Server $1$ & Server $2$ and then compare$)$

a$.$ Average length of the queue $(2$ marks$)$

b$.$ Average waiting time in the queue $(2$ marks$)$

c$.$ Average waiting time in the system $(2$ marks$)$

d$.$ Average utilization $(2$ marks$)$

e$.$ Average number of busy servers $(2$ marks$)$