Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and the next. The duration of a phone call is assumed to be distributed exponentially with mean 3 minutes. Find the following. (g) Estimate the fraction of a day that the server is busy.
Explanation
The utilization factor (ρ) is used to estimate the fraction of time the server is busy. It is calculated as the product of the arrival rate (λ) and the service rate (μ). In this case, λ = 1/10 and μ = 1/3, resulting in ρ = 1/30. This means the server is busy for 1/30 of the day.
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