Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.Determine the average time a customer spends in the system.
A)30 minutes
B)20 minutes
C)45 minutes
D)15 minutes

Question

Quizplus · Accepted Answer

Given the arrival rate ($\lambda$) is 10 customers per hour and the mean service time ($\mu$) is 5 minutes (or 12 customers per hour since 60 minutes / 5 minutes = 12), we can use the formula for the average time a customer spends in the system in a M/M/1 queue: $T = \frac{1}{\mu - \lambda}$. Substituting the given values, $T = \frac{1}{12 - 10} = \frac{1}{2}$ hour, or 30 minutes.

Customers at an Amusement Park Arrive at the Rate of 10