A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 2.5 per minute. In serving themselves, customers take about 20 seconds, exponentially distributed. a. How many customers would you expect to see, on average, at the coffee urn

There will be 5 customers on average at the coffee urn at any time.

Explanation:

The waiting line model explains that the average number of customers im the system at any time, L, is related to the average rate of arrivals of customers, λ and the average service rate, μ through the relation

L = λ ÷ (μ - λ)

L = ?

λ = 2.5 customers per minute

Each customer spends an average of 20 seconds in the shop.

Time spent in the shop = 20 seconds per customer = (20/60) minutes per customer = 0.333333 minutes per customer.

μ = (1/0.3333) = 3 customers are in the shop per minute.

L = λ ÷ (μ - λ)

L = 2.5 ÷ (3 - 2.5)

L = 5 customers.

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