Compound TCP with Random Early Detection (RED): stability, bifurcation and performance analyses
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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.
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