Consider an espresso stand with a single barsita.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 minute.If the arrival rate remains at 28 customers per hour and the stand's manager wants to have the average time a customer spends in the system i.e. ,wait time line and service time)to be a maximum of 6 minutes on average,then the service rate must
A)decrease by 2 to 33 customers per hour
B)decrease by 3 to 32 customers per hour
C)increase by 3 to 38 customers per hour
D)increase by 2 to 37 customers per hour

Question

Quizplus · Accepted Answer

We can calculate the average time a customer spends in the system (wait time + service time) as:

W = (1 / (μ - λ)) + (1 / μ)

Where λ is the arrival rate, and μ is the service rate.

Plugging in the given values, we have:

W = (1 / (35/60 - 28)) + (1 / 35/60)
W = 4.8 minutes

This means that currently, the average time a customer spends in the system is 4.8 minutes.

To have the average time a customer spends in the system to be a maximum of 6 minutes on average, we need to increase the service rate.

Solving for μ in the above equation with W = 6, we get:

μ = 38 customers per hour

Therefore, the service rate must increase by 3 to 38 customers per hour, which is answer choice C.

Consider an Espresso Stand with a Single Barsita