Tasks that are initiated when a threshold is crossed execute as background tasks. These tasks do not have an associated terminal or user session. If you execute sp_who while these tasks are running, the status column shows “background”.
The SAP ASE server executes the threshold procedure with the permissions of the user who modified the threshold, at the time he or she executed sp_modifythreshold, minus any permissions that have since been revoked.
Each threshold procedure uses one user connection, for as long as it takes to execute the procedure.