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The reference desk of a university library receives requests for assistance
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.
d. What is the average time at the reference desk in minutes (waiting time plus service time)?
Expert Solution
Computation of Average Time at the reference desk in minutes (waiting time plus service time):
Given,
Arrival rate, λ = 10 requests per hour
Service rate, μ = 12 requests per hour
Average Time at the reference desk in minutes (W) = Wq + 1/µ
= 0.4167 + (1/12)
= 0.4167 + 0.0833
= 0.5 hours or 30 minutes
Workings:
First we calculate Average number of requests that will be waiting for service (Lq):
Average number of requests that will be waiting for service (Lq)= λ^2 / [µ (µ-λ)]
= 10^2 / [12 *(12-10)]
= 100 / (12*2)
= 100/24
Average number of requests that will be waiting for service (Lq)= 4.1667 requests
Now we calculate Average number of requests that will be waiting for service (Wq):
Average number of requests that will be waiting for service (Wq) = λ /µ * (µ - λ)
= 10 / 12*(12-10)
= 10 / 12*2
= 10 / 24
Average number of requests that will be waiting for service (Wq) = 0.4167 hours or 25 minutes
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