service's been down

english-test.net/toeic/liste … ernet.html

Please explain : to be down in the sentence:
The server’s been down all morning.

and service’s = ‘service is’ or ‘service has’?

Thank You.

The service has been down all morning.

The ‘service’ is a telephone/network/ internet connection or similar. When this type of service is ‘down’, there is no connection available (the line is down - the connection is not working).

The server has been down all morning.
As above, there is no connection available through the network server. It is down, ie. for some reason it is not working.