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)

Please, if you have readings about transmission media and telephone systems, either in the library or on the Internet, for this question, please list them.

Explanation / Answer

Step-1:Given each telephone makes 0.5 calls/hour at 6 minutes each.

i.e, average telephone is used to make five calls per 8-hour workday

      8hrs-à5 calls

       1hr-à?

Then we get 0.5calls/hour.

Thus, a telephone occupies a circuit for 0.5*6=3min/hr.

Step-2: Given a simple telephone system consists of two end offices and a single toll office to which each end office is connected .

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.

20/10%=20/10/100=200telephones.

Step-3: Given the interoffice trunk has 1Mhz= 1,000,000/4000(4Khz) = 250 circuits multiplexed onto it.

Step-4:With 200 telephones per circuit, an end-office can support 200x250 = 50,000 telephones.

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