The reference desk of a university library receives requests for assistance. Ass

Question

The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 12 requests per hour.

What is the probability that no requests for assistance are in the system? If required, round your answer to four decimal places.

P0 =

What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.

Lq =

What is the average waiting time in minutes before service begins? If required, round your answer to four decimal places.

Wq =  hours

What is the average time at the reference desk in minutes (waiting time plus service time)? If required, round your answer to one decimal place.

W =  hours

What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.

Pw =

Explanation / Answer

Here in the question lambda = 10 requests per hour

and mu = 12 requests per hour

therefore P0 = 1 - 10/12= 0.167

Ls= average number of units (requests) in the system = 10 / (12-10) = 5

Ws= average time a unit spends in the system = 1 / (12-10) = 0.5

Lq= average number of units waiting in the queue = 10^2 / 12*(12-10) = 4.167

Wq= average time a unit spends waiting in the queue = 10 / 12*(12-10) = 0.4167

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