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On average how many requests are in the first department (including those who are waiting) is 1.32.

Step-by-step explanation:

In this case, use the Little's law of queuing theory.

The Little's law states that the average number of customers in a fixed system (L) is equal to the average effective arrival rate (λ) multiplied by the average time a customer spends in the system (W).

The number of requests per hour in the 1st department is, λ₁ = 4.

It is provided that 20% are rejected directly by the 1st department without going into the 2nd department.

Then the number of requests per hour is, λ₂ =

The average time a customer spends in the 1st department,

W₁ = 20 minutes = 0.33 hours.

The average time a customer spends in the 1st department,

W₂ = 60 minutes = 1 hour

On average how many requests are in the first department (including those who are waiting) is:

L = λ₁ × W₁

  = 4 × 0.33

  = 1.32

Thus, on average how many requests are in the first department (including those who are waiting) is 1.32.