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 there are more than 2 customers in the system is
A)0.128
B)0.488
C)0.512
D)0.640

Question

Quizplus · Accepted Answer

The system is an M/M/1 queue. The traffic intensity, ρ, is λ/μ = 28/35 = 0.8. The probability of having more than 2 customers in the system is 1 - P(0) - P(1) - P(2), where P(n) = (1-ρ)ρ^n. Calculating gives P(0) = 0.2, P(1) = 0.16, P(2) = 0.128. Thus, the probability of more than 2 customers is 1 - (0.2 + 0.16 + 0.128) = 0.512.

Consider an Espresso Stand with a Single Barista