Consider an espresso stand with a single barista. Customers arrive to the stand at the rate of 28 per hour according to a Poisson distribution. Service times are exponentially distributed with a service rate of 35 customers per hour. The probability that the server is busy and a customer will have to wait is
A) 0.20.
B) 0.60.
C) 0.80.
D) 1.00.

Question

Quizplus · Accepted Answer

The probability that the server is busy is the utilization factor, calculated as the arrival rate (λ) divided by the service rate (μ). Here, λ = 28 customers/hour and μ = 35 customers/hour. Utilization = λ/μ = 28/35 = 0.80.

Consider an Espresso Stand with a Single Barista