A simple telephone system consists of two end offices and a single toll office t

Question

A simple telephone system consists of two end offices and a single toll office to which each end office is connected by a 1-MHzfull-duplex trunk. The average telephone is used to make five calls per 8-hour workday. The mean call duration is 6 min. Ten percent of the calls are long distance (i.e., pass through the toll office). What is the maximum number of telephones an end office can support? (Assume 4 kHz per circuit, and note that you may need to do some additional readings about transmission media and telephone systems, either in the library or on the Internet, for this question. Please list what you read if this is the case.)

Explanation / Answer

Each telephone makes 0.5 calls/hour at 6 minutes each.

Thus, a telephone occupies a circuit for 3 min/hour.

Twenty telephones can share a circuit. Since 10% of the calls are long

distance, it takes 200 telephones to occupy a long-distance circuit full time. The interoffice

trunk has 1,000,000/4000 = 250 circuits multiplexed onto it. With 200 telephones per circuit,

an end-office can support 200x250 = 50,000 telephones.

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