Telephone calls arrives at telephone booth following Poisson distribution at an average of 5 minutes between one and next. The length of phone call is assumed to be experientially distributed with an average of 4 minute What is the probability that a person arriving at the booth will have to wait? What is the average length of queue that forms time to time?

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Telephone calls arrives at telephone booth following Poisson distribution at an average of 5 minutes between one and next. The length of phone call is assumed to be experientially distributed with an average of 4 minute  What is the probability that a person arriving at the booth will have to wait? What is the average length of queue that forms time to time?

Suresh Chand · Accepted Answer

Solution: λ = 1 call per minute = 1 / 5 per minute   μ = 1 call per 4 minute = 1 / 4 per minute   i) Probability that server is busy (ρ) = (frac{λ}{μ}) = (frac{frac{1}{5}}{frac{1}{4}}) = 0.8 ii) Average length of queue (Lq) = (frac{ρ^2}{1-ρ}) = (frac{0.64}{1-0.8}) = 3.2

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