Consider a simple telephone network consisting of two end st

Consider a simple telephone network consisting of two end stations and one intermediate switch with full - duplex trunk between each end office and the intermediate switch. An average telephone is used to make four calls per 8 hour work day with a mean call distribution of 8 minutes. 20% of the calls are long distance.The end office can support a maximum number of 15,000 calls and if the channel bandwidth for a telephone call is 4KHz, what is the capacity of the full - duplex trunk between the end office and the intermediate switch?

Solution

Each telephone makes 0.5 calls/hour at 6 minutes each. Thus a telephone occupies a circuit for 3 minutes per hour. Twenty telephones can share a circuit (although this 100% utilization implies long queuing delays). Since 10% of the calls are long distance, it takes 200 telephones to occupy a long distance (4 kHz) channel full time. The interoffice trunk has 10^6/(4 × 10^3) = 250 channels. With 200 telephones per channel, an end office can support 200 × 250 = 50,000 telephones. Source