Question

An espresso stand has a single server. Customers arrive to the stand at the rate of 20 per hour according to a Poisson distribution. Service times are exponentially distributed with a mean service time of 2 minutes per customer. The service rate per hour for the espresso stand is

Answer 1

Answer:

$\rho=0.6667$

Step-by-step explanation:

Given that

Arrival rate ,λ = 20 per hour

Service rate ,μ = 2 min per customer

$\mu=\dfrac{60}{2}\ customer/hour$

μ =3 customer per hour

The service rate ρ is given as follows

$\rho=\dfrac{\lambda }{\mu}$

Now by putting the values in the above equation we get

$\rho=\dfrac{20}{30}$

$\rho=0.6667$

Therefore the service rate will be 0.667