Question

A petrol pump station has 4 pumps. The service times follow the exponential distribution with a mean of 6 minutes, and cars arrive for service in a Poisson process at the rate of 30 cars per hour. What is the probability that an arrival would have to wait in line?

Answer 1

The probability that an arrival would have to wait in line at the petrol pump station is 0.09091.

Step-by-step explanation:

In order to find the probability that an arrival would have to wait in line, we need to calculate the utilization of the petrol pump station. Utilization is defined as the ratio of the arrival rate to the service rate. In this case, the arrival rate is 30 cars per hour and the service rate is 1 car every 6 minutes (since the mean service time is 6 minutes). So, the utilization is (30/60) * (1/6) = 0.08333.

The probability that an arrival would have to wait in line is given by the formula:

P(waiting) = Utilization / (1 - Utilization)

Plugging in the value of utilization, the probability of waiting is:
P(waiting) = 0.08333 / (1 - 0.08333) = 0.09091.