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 in the system?
A)0.43
B)1.67
C)0.57
D)1.33
E)None of the above

Question

Quizplus · Accepted Answer

Utilization, ρ = λ/μ = 4/7
Average number of customers in the system, Ls = λ/(μ-λ) = 4/3
So, the average number of customers in the system is 1.33, which is Option D.

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