All you want to know - or not(!), can be found at the sited website.
www.amc.af.mil/amctravel/
For your entertainment, I have extracted the following:
SPACE AVAILABLE TRAVEL ELIGIBILITY
A complete listing of eligible passengers by category is contained in DoD 4515.13-R.
The following is a partial listing of eligible individuals.
Category I:
Emergency travel in connection with serious illness, death, or impending death of a member of the immediate family of the following:
United States citizen civilian employees of the DoD stationed overseas.
Full-time, paid personnel of the American Red Cross serving with United States military services overseas.
Uniformed service family members whose sponsors are stationed within the Continental United States (CONUS) and the emergency exists overseas.
Family members of United States citizen civilian employees of the DoD when both sponsor and dependents are stationed overseas at the same location.
Category II:
Sponsors on environmental and morale leave (EML) and accompanied family members.
DoD Dependent School (DoDDS) teachers and their accompanied family members in EML status during school year holiday or vacation periods.
Category III:
Members of the uniformed services in an ordinary or re-enlistment leave status and uniformed services patients on convalescent leave. Members on convalescent leave may not travel overseas unless their leave form is so annotated.
Military personnel traveling on permissive temporary duty (TDY) orders for house hunting.
If the permissive TDY is for the purpose of permanent change of station house hunting, the member travels in Category III and can be accompanied by one family member.
Dependents of military members deployed for more than 365 consecutive days.
Bona fide family members (up to age 23 with a valid identification card) of a service member of the uniformed services when accompanied by their sponsor who is in an ordinary leave status within overseas areas between overseas stations and air terminals in the CONUS.
This privilege does not apply to travel of dependents to or from a sponsor's restricted or unaccompanied tour location or to travel in a leave status to or from TDY locations. It applies only to round-trip travel to an overseas area or the CONUS with the sponsor. DoD 4515.13-R restricts use of these privileges to establish a home for family members in an overseas area or the CONUS.
Foreign exchange service members on permanent duty with the DoD, when in a leave status.
Category IV:
Dependents of military members deployed for more than 120 consecutive days.
Unaccompanied family members (18 years or older) traveling on EML orders. Family members under 18 must be accompanied by an adult family member who is traveling EML.
DoDDS teachers or family members (accompanied or unaccompanied) in an EML status during summer break.
Category V:
Unaccompanied Command-sponsored dependents.
Students whose sponsor is stationed in Alaska or Hawaii.
Students enrolled in a trade school in the CONUS when the sponsor is stationed overseas.
Military personnel traveling on permissive TDY orders for other than house hunting.
Category VI:
National Guard/Reserve components/members of the Ready Reserve and members of the Standby Reserve who are on the Active Status List.
Retired military members who are issued DD Form 2 and eligible to receive retired or retainer pay.
Family members (with a valid identification card) of retired members when accompanied by a sponsor.
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