Is sharing with retransmissions causing instabilities?

Retransmissions represent a primary failure recovery mech- anism on all layers of communication network architecture. Similarly, fair sharing, e.g. processor sharing (PS), is a widely accepted approach to resource allocation among mul- tiple users. Recent work has shown that retransmissions in failure-prone, e.g. wireless ad hoc, networks can cause heavy tails and long delays. In this paper, we discover a new phe- nomenon showing that PS-based scheduling induces com- plete instability in the presence of retransmissions, regard- less of how low the traffic load may be. This phenomenon occurs even when the job sizes are bounded/fragmented, e.g. deterministic. Our analytical results are further validated via simulation experiments. Moreover, our work demon- strates that scheduling one job at a time, such as first-come- first-serve, achieves stability and should be preferred in these systems.