A ticket office has three agents answering incoming phone calls. In addition, one caller can be...

  

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A ticket office has three agents answering incoming phone calls. In addition, one caller can be put in a waiting line if all agents are busy. If all four lines (three agents plus one waiting line) are busy, the caller gets a busy signal and just calls another ticket office; so that customer is lost. Calls arrive according to a Poisson process, 20 per hour on average. The length of a call is 3 minutes on average, exponentially distributed. What is the (long-run) probability that a. a caller gets through immediately? b. a caller will be put in the waiting line? c. a caller is lost because of busy lines? A ticket office has three agents answering incoming phone calls. In addition, one caller can be put in a waiting line if all agents are busy. If all four lines (three agents plus one waiting line) are busy, the caller gets a busy signal and just calls another ticket office; so that customer is lost. Calls arrive according to a Poisson process, 20 per hour on average. The length of a call is 3 minutes on average, exponentially distributed. What is the (long-run) probability that a. a caller gets through immediately? b. a caller will be put in the waiting line? c. a caller is lost because of busy lines?