Customers enter the waiting line at a cafeteria on a first-come, first-served basis.The arrival rate follows a Poisson distribution, while service times follow an exponential distribution.If the average number of arrivals is four per minute and the average service rate of a single server is seven per minute, what is the average number of customers waiting in line behind the person being served?
A)0.76
B)0.19
C)1.33
D)1.67

Question

Quizplus · Accepted Answer

The average number of customers waiting in line 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 λ = 4 and μ = 7, we get Lq = 4^2 / (7(7 - 4)) = 16 / 21 = 0.76.

Customers Enter the Waiting Line at a Cafeteria on a First-Come