There are couple of ways that you can restrict access to a database :
- Using LOGON Trigger - but only temporarily (enable before upgrade and then disable it). Refer to my answer
here for more details including a script.
- You can shutdown IIS on the webservers so that no connections are made using the application. This is called "Applicaiton downtime"
Keep database in single user mode using (Note this will be risky as if there is any other connection to the database then you might
end up waiting or refused connection.)
alter database databasename
set single_user with rollback immediately
You are better off using Option 2 as a safe and planned upgrade during your maintenance window.
Restricted user - only users with dbo rights on database allowed (e.g. db_owner,
dbcreator, sysadmin). This means that multiple users can still be logged into the database, as long as they are DBO.
Single user - only one connection allowed i.e. first come, first served.
Due to the fact that Single user will be first come, first served -- it will be more risky in case of error or somehow your connections gets terminated.
When dealing with Logon Trigger, as @AaronBertrand pointed out, that it will not work for existing sessions, but you can over come that by first killing all the sessions and then enabling the trigger so that all the new incoming connections have to go through the trigger.
I can't think of any other way of restricting the connections to the database.