Solution :
The average number of the arrivals, λ = 6 per hour
Average service rate, [tex]$\mu = \frac{60 \times 2}{15}$[/tex]
= 8
Average number of the customers in the system is given by,
[tex]$= \frac{\lambda}{\mu - \lambda }$[/tex]
[tex]$= \frac{6}{8 - 6 }$[/tex]
= 3
Average number of the customers that are waiting in the line behind the person who are being served is,
[tex]$=\frac{\left(\frac{\lambda}{\mu}\right)^2}{1-\frac{\lambda}{\mu}} $[/tex]
[tex]$=\frac{\left(\frac{6}{8}\right)^2}{1-\frac{6}{8}} $[/tex]
[tex]$=\frac{(0.75)^2 }{0.25} $[/tex]
= 2.25
Proportion of the time the server is busy,
[tex]$=\frac{\lambda}{\mu}$[/tex]
[tex]$=\frac{6}{8}$[/tex]
= 0.75
