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hw1q5ee555 - 5 A Company has a system of 4"private...

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5. A Company has a system of 4 "private" telephone lines (each line constitutes a "server") connecting two of its sites. Suppose that requests for calls arrive according to a Poisson process at a rate of 1 call every two minutes. Call durations (i.e. service times) are exponentially distributed with mean of 4 minutes. Two models are to be considered as follows a) When all lines are busy, the system "delays" (i.e. queues) the call requests until a line become available. Assume an infinite-size queue. Find 1. The probability of having to wait for a line 2. The average number of calls waiting in the queue and the mean waiting time in the queue 3. The probability that there will be two calls waiting in the queue given that the buffer is not empty. 4. The average number of idle lines. b) When all lines are busy, the system automatically redirects new calls to the public switched telephone network (PSTN). Find 1. The proportion of the calls that are redirected to the PSTN 2. The average number of busy lines in the private system
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