IMSI is used by UE in attach request very first time when it does attach. Once the UE gets admitted in network afterwards UE uses GUTI whenever UE identity needs to be send. I never heard about TMSI used in LTE network however S-TMSI is part of GUTI and used in rrc connection request message as initial UE identity.
GUTI = GUMMEI + M-TMSI .
S-TMSI = MMEC + M-TMSI.
Both M-TMSI and S-TMSI identifiers are constructed from GUTI and GUTI is allocated to UE during the attach procedure in "Attach Accept" message.
