Performance tradeoffs in structured peer to peer streaming

We consider the following basic question: a source node wishes to stream an ordered sequence of packets to a collection of receivers, which are in K$K$ clusters. A node may send a packet to another node in its own cluster in one time step and to a node in a different cluster in _Tc$T_c$ time steps (_Tc>1)$(T_c>1)$. Each cluster has two special nodes. We assume that the source and the special nodes in each cluster have a higher capacity and thus can send multiple packets at each step, while all other nodes can both send and receive a packet at each step. We construct two (intra-cluster) data communication schemes, one based on multi-trees (using a collection of d$d$-ary interior-disjoint trees) and the other based on hypercubes. The multi-tree scheme sustains streaming within a cluster with O(dlogN)$O(dlogN)$ maximum playback delay and O(dlogN)$O(dlogN)$ size buffers, while communicating with O(d)$O\left(d\right)$ neighbors, where N$N$ is the maximum size of any cluster. We also show that this protocol is optimal when d=2$d=2$ or 3. The hypercube scheme sustains streaming within a cluster, with O(log²(N))$O\left({log}^2\left(N\right)\right)$ maximum playback delay and O(1)$O\left(1\right)$ size buffers, while communicating with O(log(N))$O(log\left(N\right))$ neighbors, for arbitrary N$N$. In addition, we extend our multi-tree scheme to work when receivers depart and arrive over time. We also evaluate our dynamic schemes using simulations.