In an ATM booth, the arrival distribution of customers follows Poisson distribution with an arrival rate of 10 customers per 2 hours. The distribution of service time follows. Exponential distribution with an average service time of 3 minutes per customers. a) Average time a customer spends in waiting line waiting for service. b) Average number of customer in waiting line for service. c) Average number of customers in the system. d) Probability that a person arriving at the booth will get service instantly. e) Probability that a customer spends more then 10 minutes the system.
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The service rate Ī¼ is 1 customer per 3 minutes, which is 20 customers per hour. The traffic intensity Ļ is Ī»/Ī¼ = 5/20 = 0.25. The average time a customer spends in the waiting line is Ļ/(Ī¼*(1-Ļ)) = 0.25/(20*(1-0.25)) = 0.0167 hours = 1 minute. Show moreā¦
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