Consider an espresso stand with a single barista.Customers arrive at 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 in the system (i.e. ,waiting and being served)is
A)0.114 minute
B)0.143 minute
C)6.84 minutes
D)8.58 minutes

Question

Quizplus · Accepted Answer

First step is to calculate the utilization factor:
 
U = λ/μ = 28/35 = 0.8
 
Then, we calculate the average time spent in the system:
 
W = 1/(μ-λ) = 1/(35-28) = 1/7 hour
 
Converting to minutes:
 
W = (1/7)*60 = 8.57 minutes ≈ 8.58 minutes
 
Therefore, the answer is D) 8.58 minutes.

Consider an Espresso Stand with a Single Barista