Add upstream length as attribute to points

[LornaMurison]

Hello,
I have a geometric network representing streams.  I also have a series of points along that stream network.  For each point I would like to know the total length of streams draining to that point.
Any ideas?  This would need it to be automated so I don't have to manually add a flag for each one of my points.
Thank-You.

[LornaMurison]

A flowaccumulation grid with initial conditions placing one unit of rainfall within the streams and zero units outside

Thank-you for your reply.
Could you be more specific about how this is done?
The actual distance itself is not important, all I need is a way to measure which point is upstream or downstream of another point.

[LornaMurison]

No, the points are not all on the same stream segment or tributary, they are all over the place.  But I do not need to know how each point relates to every other point, only how 3 or so relate to each other.  Each point is the intersection of the edge of a lake and the streams layer.  I need to find the point that represents the outlet of the lake, so that I can delineate a catchment.  I would like to do this, essentially, by taking all points with the same LakeID and finding the one with the greatest flow accumulation.
Thank-you for your help, let me know if you need any more explanation.