What are messages transferred between MME-HSS?

Question

Please describe the name of the messages between MME-HSS.

Answer 1

Couple of messages are exchanged between MME and HSS during attach procedure for an UE. The very first messages exchanged between MME and HSS are Authentication-Information-Request and Authentication-Information-Answer.

Following messages are defined between MME and HSS.
MME initiated
1.Update-Location-Request/Answer
2.Notification-Request/Answer
3.Purge-Request/Answer.
4. Autthentication-Information-Request/Answer

HSS initiated
1.Insert-Subscription-Data-Request/Answer
2.Delete-Subscriber-Data-Request/Answer
3. Cancel-Location-Request/Answer
4. Reset-Request/Answer

References:
3GPP TS 29.272

Answer 2

There are many messages exchanged between them as pointed out by our friend Vimal. Some of them are listed below.

1)AIR/AIA (Authentication-Information-Request/Answer):- MME fetches Authentication data from HSS to authenticate subscriber.

2)ULR/ULA (Update-Location-Request/Answer):- MME stores its own identity at HSS, and fetches subscription data from HSS.

3)NOR/NOA (Notification-Request/Answer):- MME stores PDN address and other attach information at HSS.

4)PUR/PUA (Purge Request/Answer):- MME informs the HSS that UE is inactive for a long period and that's why MME has deleted the Subscription Data received in previous ULR from its end.

5)IDR/IDA(Insert-Subscription-Data-Request/Answer):- It is invoked by HSS only when a subscriber is attached and there is change in subscriber profile at HSS end then same change to be reflected at Subscriber profile at MME (sent in ULA) end as well.

6)DSR/DSA (Delete-Subscriber-Data-Request/Answer):- It is invoked by HSS only when Subscriber is attached and some data is deleted at HSS. Now HSS informs MME with this message that some part of subscription data is deleted at HSS.

7)CLR/CLA(Cancel-Location-Request/Answer):- Invoked by HSS to detach the subscriber.

8)RSR/RSA(Reset-Request/Answer):- Invoked by HSS, to inform MME that HSS goes down for some time, kindly sync the data and send fresh location/PDN information at HSS.

Please refer specifications of the DIAMETER Protocol for a detailed description of all the messages.
A good guide is available here -> http://diameter-protocol.blogspot.in/2012/07/s6as6d.html

Happy reading : )