In live streaming systems (IPTV, life-stream services, etc.), an attractive
service consists in allowing users to access past portions of the stream. This
is called a time-shifted streaming system. In our vision, a centralized
time-shifted streaming system face scalability and ethical issues, therefore,
we address the problem of designing a peer-to-peer system where peers store and
deliver past chunks. We first attempt to identify the main characteristics of
time-shifted streaming system from well-known measurements of VoD and IPTV
systems. These overlays are the first structures specifically designed for
time-shifted streaming system. Although no evaluation is presented, these
preliminary description aim to foster discussions on a critical service.