Hi Arcady,
You can see the individual publication last upload and last download times in the ml_subscription MobiLink server system table:
e.g.
SELECT name, remote_id, publication_name, last_upload_time, last_download_time
FROM ml_subscription join ml_database join ml_user;
name,remote_id,publication_name,last_upload_time,last_download_time
'rem1','38e3493e-6bf5-45be-93d0-b4b38852fb8a','p1','2015-02-18 11:26:33.545','1900-01-01 00:00:00.000'
Where all of these are the last committed times (the upload time is end of the last upload, the download time is the last confirmed value from the remote when it uploaded ).
Since that may not be what you want, you could also create some custom logic to record when clients come in to connect to MobiLink using the begin_synchronization connection event.
Regards,
Jeff Albion
SAP Active Global Support