  Retransmissions represent a primary failure recovery mechanism on all layers
of communication network architecture. Similarly, fair sharing, e.g. processor
sharing (PS), is a widely accepted approach to resource allocation among
multiple 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 phenomenon showing that PS-based scheduling induces
complete instability with zero throughput in the presence of retransmissions,
regardless 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
demonstrates that scheduling one job at a time, such as first-come-first-serve,
achieves stability and should be preferred in these systems.
