Question

A simple telephone system consists of a single toll office and two end offices, each connected to the toll office with N telephones. The wires between each end office and the toll office has 1 MHz capacity in each direction and each active telephone call requires 5 kHz bandwidth. 10% of the calls are long distance (calls that do not pass through the toll office are ‘local calls’, e.g. phone calls within the network, while calls that do pass through the toll office are ‘long distance calls’). On average, each telephone is used to make 4 calls between 9 AM and 5 PM. The mean of call duration is 8 mins.

1. Will the local calls occupy the bandwidth between the end office and toll office? Why?

2. What is the maximum number of telephones, N, that an end office can support? (for this problem, don’t worry about the blocking probability and the bandwidth between telephones and the end office.)

3. Assume that among these long distance calls, there are 80% are voice calls and 20% are video calls. The average duration for a voice call is 3 mins, and the average duration a video call is 50 mins. At a specific moment, what percentage of long distance calls are video calls?

Answer 1

1. Will the local calls occupy the bandwidth between the end office and toll office? Why?

No, the local calls will not occupy the bandwidth between the end office and toll office as local calls do not pass through the toll office.

2. What is the maximum number of telephones, N, that an end office can support?

Since 4 calls are made between 9 am to 5 pm i.e. 8 hours therefore 0.5 calls are made per hour with mean time of 8 minutes.

The number of long-distance calls = 4*0.10 = 0.4

Per day average long-distance call = 8*0.4 = 3.2

Number of user end office can support in a day = (8*60) / (3.2) = 150

Number of simultaneous channels end office support = 1Mhz /5 KHz = 200

Maximum number of telephones that an end office can support = 200 * 150 = 30000

3. Assume that among these long distance calls, there are 80% are voice calls and 20% are video calls. The average duration for a voice call is 3 mins, and the average duration a video call is 50 mins. At a specific moment, what percentage of long distance calls are video calls?

The percentage of long-distance calls that are video calls = 20

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