Question

in a railway marshallimg yard trains arrive at the rate of 30 trains per day. assuming that arrival time follows an poisson distribution is exponention and the service time distribution is exponential with an average of 36 minutes. Find the length of the system.


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Answer 1

Answer:

(i) Average number or trains in the queue is

E(m)=(λ2 )/(μ(μ-λ))

λ=30/(60x24)=1/48 trains per minute

E(m)=((1/48)2 )/(1/36(1/36-1/48))=108/48=2.25 or rounghly 2 trains

(ii) The probability that number or trains in it system exceeds 10

P(≥10)=P10 =(λ/μ)10=((1/48)/(1/36))10=(0.75)10 =0.06