As a customer service personnel, what to do if I could not reach a particular customer at a point time due to network failure and customer comes shouting?

Being transparent with the customers builds the trust relationship more strong.  We have to confess the delays even if its a network issue and apologize with customer.  Eventually he will be satisfied with what you says and he will cool-down, he feels that you are trying your best to attend him; also it will creates long-term customer relationship.