Here is some brief information for you:
1. Explicit IMSI detach: the MS informs the network that it will leave the network (turn off by the power button), so the network knows the status of the MS is detached. The detached flag for this subscriber will be set in the VLR. When there is an MTC, the network will immediately informs the calling party that “The subscriber you have called is not available” without any paging procedure.
2. Implicit IMSI detach: the MS leave the network without any confirmation (for example due to lost of radio coverage, empty battery…), so the network does not know the current status of the MS. When there is an MTC, the network try to perform paging the MS within the predefined timer. When this timer expired, the network will inform the calling party that the called subscriber cannot be reached.
3. Loiterimg Time: ???
4. Periodic location timer: to prevent the lost of radio resource for paging procedure in case the MS is detached but the network does not know its status, the is the timer called “Periodic location timer” (this is T3212 timer in the ETSI spec). In the idle status, the MS has to perform the periodic location updating when the T3212 timer expired, and the network also monitors this event. If the T3212 expires but the MS does not perform the periodic location updating procedure, the network will treat that it is detached, and then doesnot perform any paging procedure when there is an MTC.
Sorry for my bad english.