  Due to missing IP multicast support on an Internet scale, over-the-top media
streams are delivered with the help of overlays as used by content delivery
networks and their peer-to-peer (P2P) extensions. In this context,
mesh/pull-based swarming plays an important role either as pure streaming
approach or in combination with tree/push mechanisms. However, the impact of
realistic client populations with heterogeneous resources is not yet fully
understood. In this technical report, we contribute to closing this gap by
mathematically analysing the most basic scheduling mechanisms latest deadline
first (LDF) and earliest deadline first (EDF) in a continuous time Markov chain
framework and combining them into a simple, yet powerful, mixed strategy to
leverage inherent differences in client resources. The main contributions are
twofold: (1) a mathematical framework for swarming on random graphs is proposed
with a focus on LDF and EDF strategies in heterogeneous scenarios; (2) a mixed
strategy, named SchedMix, is proposed that leverages peer heterogeneity. The
proposed strategy, SchedMix is shown to outperform the other two strategies
using different abstractions: a mean-field theoretic analysis of buffer
probabilities, simulations of a stochastic model on random graphs, and a
full-stack implementation of a P2P streaming system.
