Hello, 2 hints from the UK on mobile phones that may help.
1) Text messaging takes far less band width and can slip through when all you get is a network busy message with a voice call, though even these tiny SMS messages can be badly delayed.
2) Your own local Govt. may have a contract with one/more mobile operators that give them priority bandwidth during a crisis. If so it would probably be best to avoid that particular provider.
Cheers