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 $10$ kHz bandwidth.

$15\%$ 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 $16$ calls

between $9$ AM and $5$ PM$.$ The mean of call duration is $4$ mins