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We study the performance of Compound TCP with Random Early Detection (RED) in three different limiting regimes. In the first regime, averaging over the queue size helps to decides the probability of dropping packets. Then, we consider a model where averaging over the queue size is not performed, but the queue is modelled as an integrator. Finally, we consider a model where the threshold for dropping packets is so small that it is not possible to model the queue as an integrator. In these three regimes, we derive sufficient, as well as necessary and sufficient conditions for local stability. These conditions help to capture the dependence of protocol and network parameters on system stability. We also show that in the event of loss of local stability, the Compound TCP-RED system undergoes a Hopf bifurcation which would lead to limit cycles. Some of the analytical results are corroborated using packet-level simulations.

SUMMARY For ergodic birth‐death processes a lower bound for the variance of an unbiased estimator of a function of birth and death parameters is obtained under an arbitrary stopping rule. All efficiently estimable functions and closed efficient sampling schemes are characterized. The processes treated here include random walk with reflecting barriers, immigration‐death process, M/M/1 and M/M/S queues with limited or unlimited waiting space.