18-73. A small post office has two open windows. Customers arrive according to a Poisson distribution...

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18-73. A small post office has two open windows. Customers arrive according to a Poisson distribution at the rate of 1 every 3 minutes. However, only 80% of them seek service at the windows. The service time per customer is exponential, with a mean of 5 minutes. All arriving customers form one line and access available windows on a FIFO basis. (a) What is the probability that an arriving customer will wait in line? (b) What is the probability that both windows are idle? (c) What is the average length of the waiting line? (d) Would it be possible to offer reasonable service with only one window? Explain. 18-73. A small post office has two open windows. Customers arrive according to a Poisson distribution at the rate of 1 every 3 minutes. However, only 80% of them seek service at the windows. The service time per customer is exponential, with a mean of 5 minutes. All arriving customers form one line and access available windows on a FIFO basis. (a) What is the probability that an arriving customer will wait in line? (b) What is the probability that both windows are idle? (c) What is the average length of the waiting line? (d) Would it be possible to offer reasonable service with only one window? Explain.