switch ‧ board /ˈswɪtʃbɔːd $ -bɔːrd/ BrE AmE noun [countable]
a system used to connect telephone calls in an office building, hotel etc, or the people who operate the system:
switchboard operators
Hundreds of callers jammed the switchboard trying to win the tickets (=there were too many calls for the switchboard to deal with) .