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 capacity utilization for the system.
A)56%
B)78%
C)83%
D)98%

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the service rate which is the reciprocal of the mean service time:

Service rate = 1/5 minutes = 0.2 customers per minute

Next, we need to calculate the traffic intensity or the utilization factor (ρ) of the system:

ρ = (arrival rate) x (service time) = (10 customers/hr) x (1/12 hr/customer) x (0.2 customers/min) = 0.1667

Therefore, the capacity utilization for the system is:

Capacity utilization = (traffic intensity) / (1 - traffic intensity) = 0.1667 / (1 - 0.1667) = 0.83 or 83%

Hence, the correct answer is C)83%.

Customers at an Amusement Park Arrive at the Rate of 10