As you have asked about the All India Institute of Medical Sciences (AIIMS) counselling dates and about open counselling, I am giving you information about it, check below for the details

Schedule for AIIMS MBBS Counselling 2016 is given here.

Proposed Counselling Schedule to be held at AIIMS, New Delhi
1st Counselling 04, 05, 07 & 08 Jul 2016
2nd Counselling 04 Aug 2016
3rd Counselling 06 Sep 2016
Open Counselling for AIIMS, Delhi 27 Sep 2016

Those called for AIIMS MBBS Counselling 2016 have to report at venue site at the time on the date as stated in the AIIMS MBBS Call Letter 2016 along with the following documents/certificates in original:

AIIMS MBBS Admit Card
Call Letter issued by AIIMS, New Delhi.
Proof of Date of Birth
Certificate/Mark sheet from the Board from which the candidate passed the 10+2
Migration certificate from the University/Board last attended the candidate.
Category Certificate (if applicable)
Current passport size photograph (front pose) 6 copies
One set of self-attested copies of all the certificates.

Counselling Process

In the counselling process, the seats to be filled by open (UR) competition would be filled up first, wherein the candidates would be called for counselling based on merit alone irrespective of whether they belong to UR, SC, ST or OBC.
Next, reservation categories like SC/ST/OBC candidates will be counselled to fill up the seats earmarked for them in their respective categories.