  We use fluid limits to explore the (in)stability properties of wireless
networks with queue-based random-access algorithms. Queue-based random-access
schemes are simple and inherently distributed in nature, yet provide the
capability to match the optimal throughput performance of centralized
scheduling mechanisms in a wide range of scenarios. Unfortunately, the type of
activation rules for which throughput optimality has been established, may
result in excessive queue lengths and delays. The use of more
aggressive/persistent access schemes can improve the delay performance, but
does not offer any universal maximum-stability guarantees. In order to gain
qualitative insight and investigate the (in)stability properties of more
aggressive/persistent activation rules, we examine fluid limits where the
dynamics are scaled in space and time. In some situations, the fluid limits
have smooth deterministic features and maximum stability is maintained, while
in other scenarios they exhibit random oscillatory characteristics, giving rise
to major technical challenges. In the latter regime, more aggressive access
schemes continue to provide maximum stability in some networks, but may cause
instability in others. Simulation experiments are conducted to illustrate and
validate the analytical results.
