A small post office has two service counters. Customers arrive according to a Poisson distribution at the rate of 1 ever

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A small post office has two service counters. Customers arrive according to a Poisson distribution at the rate of 1 ever

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A Small Post Office Has Two Service Counters Customers Arrive According To A Poisson Distribution At The Rate Of 1 Ever 1
A Small Post Office Has Two Service Counters Customers Arrive According To A Poisson Distribution At The Rate Of 1 Ever 1 (78.85 KiB) Viewed 52 times
A small post office has two service counters. Customers arrive according to a Poisson distribution at the rate of 1 every 3 minutes. However, only 80% of them seek service at the counters. The service ime per customer is exponentially distributed, with a mean of 5 minutes. All arriving customers form one line and access available counters on a FIFO basis. (a) What is the probability that an arriving customer will wait in line? (b) What is the probability that both counters are idle? (c) What is the average length of the waiting line? (d) Would it be possible to offer reasonable service with only one counter? Explain.
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