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

  1. What is the probability that a person arriving at the booth will have to wait?
  2. What is the average length of queue that forms time to time?

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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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