  Distributed live streaming has brought a lot of interest in the past few
years. In the homogeneous case (all nodes having the same capacity), many
algorithms have been proposed, which have been proven almost optimal or
optimal. On the other hand, the performance of heterogeneous systems is not
completely understood yet. In this paper, we investigate the impact of
heterogeneity on the achievable delay of chunk-based live streaming systems. We
propose several models for taking the atomicity of a chunk into account. For
all these models, when considering the transmission of a single chunk,
heterogeneity is indeed a ``blessing'', in the sense that the achievable delay
is always faster than an equivalent homogeneous system. But for a stream of
chunks, we show that it can be a ``curse'': there is systems where the
achievable delay can be arbitrary greater compared to equivalent homogeneous
systems. However, if the system is slightly bandwidth-overprovisioned, optimal
single chunk diffusion schemes can be adapted to a stream of chunks, leading to
near-optimal, faster than homogeneous systems, heterogeneous live streaming
systems.
