Question

A petrol pump station has two pumps. The

service times follows the exponential

distribution with a mean of 4 minutes and

cars arrive for service in a Poisson process at

the rate 10 cars per hour. Find the

probability of that a customer has to wait for

service.

Answer 1

 $\begin{gathered} \mu=\frac{60}{4}=15 \text { per hour } \\ \lambda=10 \text { per hour } \end{gathered}$

P(Customer has to wait for service is) $= \frac{1}{\mu-\lambda}$

$\begin{aligned} &=\frac{1}{15-10} \\ &=0.2 \end{aligned}$

Now proportion of time pumps remain idle.

So, it can be explained by formula $\frac{\lambda}{\mu}.$

$\text { i.e. } \frac{\lambda}{\mu}=\frac{10}{15}=0.66$