Is your Output transmission program being executed based on a report? Do you have any background jobs setup to transmit the Emails or faxes on a periodic time schedule?
For instance there are some reports like RSCONN01 which is used in the background to transmit messages, so if this report is being executed on a prefixed timeline then it will be sent only when the job is successfully completed.
Also, have a look at your SCOT transaction to see what is the waiting time set up there. This may also affect the performance of SOST.
/M