Exercise 4. A simple telephone system consists of a single toll office, two end offices each connected to the toll office with N telephones, just like the figure below. 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 UCI network, while calls that do pass through the toll office are 'long distance calls') The busiest time of the day for calls is 9 AM to 5 PM and 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.) 1 1 MHz 1 MHz N users End Office Toll Office End Office N users