Respuesta :
Answer:
Option b that is 1.33 is the right choice.
Step-by-step explanation:
Given:
Mean rate of arrival [tex](\lambda)[/tex] = 8 planes/hr
Service time = [tex]5[/tex] minute/plane
Mean service rate [tex](\mu)[/tex] = [tex]\frac{60}{5}[/tex] = [tex]12[/tex] planes/hr
Applying the concept Poisson-distributed arrival and service rates (exponential inter-arrival and service times)(M/M/1) process:
We have to find mean number of planes waiting to land that is mean number of customers in the queue .
Mean number of customers in queue [tex](L_q)[/tex] .
⇒ [tex]L_q=\frac{\rho \lambda}{\mu-\lambda}[/tex]
Considering, [tex]\rho=\frac{\lambda}{\mu}[/tex] , [tex]\rho[/tex] is also mean number of customers in service.
⇒ [tex]L_q=\frac{ \lambda^2}{\mu(\mu-\lambda)}[/tex]
⇒ Plugging the values.
⇒ [tex]L_q=\frac{8^2}{12(12-8)}[/tex]
⇒ [tex]L_q=\frac{64}{48}[/tex]
⇒ [tex]L_q=1.33[/tex]
So,
Mean number of planes in holding and waiting to land = 1.33
