I agree with kenb. Most of these problems are agents

It could be they don't have enough people to handle calls. How long does each call last

If they were sitting with the phone off hook it should eletronicly re hook but they could be using wrap up timers

The main phone should show the status of each agent by the light color and flashing.

Make sure call waiting is not on the phones as this could allow a call on to a busy extension if it is their turn. Do you have no answer timer set on ucd group/ extensions incase some one did not logout and it stays ringing there

“I have not failed. I've just found 10,000 ways that won't work.”