Photostream not syncing all the photos

One of the problems faced using photo stream is it doesn't sync all the existing photos into the new devices.

Photostream basically works like this

• New photos saved on the camera roll is synced to photo stream
• The photos which are synced with iTunes do not appear on photo stream in new devices
• Only photos which are not synced with iTunes appears

In short, what Photostream offers is;

• Access of all recently taken un-synced photos across devices
• But for access of old and synced photos; iTunes sync should be done