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 average time in minutes a customer spends waiting in line for service is
A)0.114 minute
B)0.143 minute
C)6.84 minutes
D)8.58 minutes

Question

Quizplus · Accepted Answer

The average time a customer spends waiting in line (Wq) in a single-server queue can be calculated using the formula Wq = λ / (μ(μ - λ)), where λ is the arrival rate and μ is the service rate. Here, λ = 28 customers/hour and μ = 35 customers/hour. Converting the result to minutes, Wq = 28 / (35 * (35 - 28)) = 6.84 minutes.

Consider an Espresso Stand with a Single Barista