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 waiting time in the system (to two decimal places)?
A) 0.90 hours
B) 0.08 hours
C) 0.13 hours
D) Cannot be determined from the information given

Question

Quizplus · Accepted Answer

The mean waiting time in the system can be found using Little's Law, which states:
L = λW
where L is the average number of customers in the system, λ is the arrival rate, and W is the average waiting time in the system.

We know λ = 12 customers per hour and μ = 20 customers per hour (since the service rate is also the departure rate in a single server system). Therefore, ρ = λ / μ = 0.6.

Using Little's Law, we can solve for W:

L = λW
W = L / λ

We also know that L = ρ / (1 - ρ) * ρ = 0.6 / (1 - 0.6) * 0.6 = 0.96

W = 0.96 / 12 = 0.08 hours

Therefore, the answer is C: 0.13 hours (rounded to two decimal places).

For a Single Server, Single Queue System with an Arrival