Analysis of TCP with an Exponential-RED (E-RED) queue management policy with two delays

We analyze Compound TCP, the default protocol in the Windows operating system, along with an Exponential-RED (E-RED) queue policy. The E-RED queue policy specially aims for high link utilization. Our setup considers two sets of TCP flows, each having a different round-trip time, operating over a single bottleneck link. For this system, we first derive a sufficient condition for local stability. The stability condition reveals that the link gain needs to scale with the maximum round-trip time in the system. Additionally, the Compound parameter α needs to be chosen judiciously if stability is to be ensured. We then computationally show that, as parameters vary, the system can undergo a Hopf bifurcation. This bifurcation alerts us about the emergence of limit cycles, in the system dynamics, as stability is just lost. Finally, we exhibit the emergence of such limit cycles, in the queue size, via packet-level simulations. These limit cycles can result in the loss of link utilization and should be avoided.