How long would it take to reach the current edge of the known observable universe, with the following bounds in mind:

• We figure out a way build a space ship to provide a constant 1 G acceleration for an extended period of time.
• We accelerate until we are halfway there, then decelerate past this point (so we stop when we get there.
• Our target is about 15 billion lightyears away. As per http://curious.astro.cornell.edu/about-us/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/616-is-the-universe-expanding-faster-than-the-speed-of-light-intermediate galaxies past 4,740 megaparsecs are no longer reachable. Using this site http://www.convertunits.com/from/megaparsecs/to/light+years to convert megaparsecs to lightyears means this "unreachable" point is currently 15,459,812,396.5002 lightyears away. Let's simplify to 15 billion lightyears, which is still supposed to be reachable.
• We somehow work out all the details of life support, collision with particles at relativistic speeds, etc...

I would like to know the time the traveler experiences, and the time that everyone else (e.g. those on earth) experience.

How long would it take to reach the current edge of the reachable portion of the universe, with the following bounds in mind:

• We figure out a way build a space ship to provide a constant 1 G acceleration for an extended period of time.
• We accelerate until we are halfway there, then decelerate past this point (so we stop when we get there.
• Our target is about 15 billion lightyears away. As per http://curious.astro.cornell.edu/about-us/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/616-is-the-universe-expanding-faster-than-the-speed-of-light-intermediate galaxies past 4,740 megaparsecs are no longer reachable. Using this site http://www.convertunits.com/from/megaparsecs/to/light+years to convert megaparsecs to lightyears means this "unreachable" point is currently 15,459,812,396.5002 lightyears away. Let's simplify to 15 billion lightyears, which is still supposed to be reachable.
• We somehow work out all the details of life support, collision with particles at relativistic speeds, etc...

I would like to know the time the traveler experiences, and the time that everyone else (e.g. those on earth) experience.