A telephone with 3 lines is modeled by the Bernoulli single-server queuing process with limited capacity...

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A telephone with 3 lines is modeled by the Bernoulli single-server queuing process with limited capacity (C= 3). If all three lines are busy, the new callers receive a busy signal and cannot enter the queue. On the average, there are 10 calls per hour, and the average call takes 5 minutes. (a) Find the transition probability matrix using one-minute frames (b) At 8:00 am there are two callers, one is being served and one is waiting. Find the probability that all three lines are busy at 8:03 am using one- minute frames. (c) Compute the steady-state probabilities using one-minute frames. A telephone with 3 lines is modeled by the Bernoulli single-server queuing process with limited capacity (C= 3). If all three lines are busy, the new callers receive a busy signal and cannot enter the queue. On the average, there are 10 calls per hour, and the average call takes 5 minutes. (a) Find the transition probability matrix using one-minute frames (b) At 8:00 am there are two callers, one is being served and one is waiting. Find the probability that all three lines are busy at 8:03 am using one- minute frames. (c) Compute the steady-state probabilities using one-minute frames.

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