Could not obtain exclusive lock on database 'model' - who is using it?
Your model database is locked now so what you should do is to find out the session that has a lock on it, this can be done using sys.dm_tran_locks:
select request_session_id
from sys.dm_tran_locks
where resource_type = 'database' and
      resource_database_id = 3 and
      request_type = 'LOCK' and
      request_status = 'GRANT';

You can have a user that just opened an SSMS query window with the context of model database and did not ever execute any query there, but that session still holds S lock on the database resource.
Once you have found the locking session, just kill it.