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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

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Answer:

[tex]\rho=0.6667[/tex]

Step-by-step explanation:

Given that

Arrival rate ,λ = 20 per hour

Service rate ,μ = 2 min per customer

[tex]\mu=\dfrac{60}{2}\ customer/hour[/tex]

μ =3 customer per hour

The service rate ρ is given as follows

[tex]\rho=\dfrac{\lambda }{\mu}[/tex]

Now by putting the values in the above equation we get

[tex]\rho=\dfrac{20}{30}[/tex]

[tex]\rho=0.6667[/tex]

Therefore the service rate will be 0.667

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