PPS I would also make NUM_ALLOWED an INT to match the data type that COUNT() returns.

And one other perfromance bump might be to capture the ORIGINAL_LOGIN() in a variable, instead of calling it twice, like so:

USE master

GO

CREATE TRIGGER connection_limit_trigger ON ALL SERVER

WITH EXECUTE AS 'logon_trigger_login'

FOR LOGON

AS

BEGIN

DECLARE @original_login SYSNAME = ORIGINAL_LOGIN();

-- the list of logins to restrict

IF (

SELECT NUM_ALLOWED

FROM GK50LIVE.dbo.LimitedLogins

WHERE LOGIN_ID = @original_login

) < (

SELECT COUNT(*)

FROM sys.dm_exec_sessions

WHERE is_user_process = 1

AND original_login_name = @original_login

)

BEGIN

ROLLBACK

END

END;

GO