For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the mean number of customers in the system (to two decimal places)?
A) 0.90
B) 0.60
C) 1.50
D) Cannot be determined from the information given

Question

Quizplus · Accepted Answer

To find the mean number of customers in the system, we need to use the Little's Law which states that the mean number of customers in the system is equal to the product of the arrival rate and the mean time a customer spends in the system.

Since this is a single server, single queue system, the mean time a customer spends in the system can be calculated as the sum of the mean time spent waiting in the queue and the mean service time.

The mean time spent waiting in the queue can be calculated using the formula Lq = λ^2 / (μ(μ-λ)), where λ is the arrival rate and μ is the service rate. 
Substituting the given values, we get Lq = (12^2) / (20(20-12)) = 2.88

The mean service time can be calculated as 1/μ = 1/20 = 0.05 hours.

Therefore, the mean time a customer spends in the system is 0.05 + 2.88 = 2.93 hours.

Using Little's Law, the mean number of customers in the system can be calculated as 12 x 2.93 = 35.16. Rounded to two decimal places, the answer is 1.50.

For a Single Server, Single Queue System with an Arrival