  The problem of increased queueing delays in the Internet motivates the study
of currently implemented transport protocols and active queue management (AQM)
policies. We study Compound TCP (default protocol in Windows) with Random Early
Detection (RED). RED uses an exponentially weighted moving average of the queue
size to make packet-dropping decisions, aiming to control the queue size. One
must study RED with current protocols in order to explore its viability in the
context of increased queueing delays.
  We derive a non-linear time-delayed model for Compound TCP-RED. We derive a
sufficient condition for local stability of this model, and examine the impact
of (i) round-trip time (RTT) of the TCP flows, (ii) queue averaging parameter
and (iii) packet-dropping thresholds. Further, we establish that the system
undergoes a Hopf bifurcation as any of the above parameters is varied. This
suggests the emergence of limit cycles in the queue size, which may lead to
synchronisation of TCP flows and loss of link utilisation. Next, we study a
regime where queue size averaging is not performed, and packet-dropping
decisions are based on instantaneous queue size. In this regime, we derive the
necessary and sufficient condition for local stability. A comparison of the
stability results for Compound TCP-RED in the two regimes--with and without
queue size averaging--reveals that averaging may not be beneficial to system
stability. Packet-level simulations show that the queue size indeed exhibits
limit cycle oscillations as system parameters are varied. We then outline a
simple threshold-based queue policy, that could ensure stable low-latency
operation. We show that the threshold policy outperforms RED in terms of
queueing delay, flow completion time and packet loss. We highlight that the
threshold-based policy could mitigate the issue of increased queueing delays in
the Internet.
