| This paper investigates the stability of TCP networks when packets are randomly dropped at bottleneck routers with a constant or near-constant probability. Analysis of a previously developed system of stochastic differential equations leads to the proposal of a new router algorithm, RWFD, which drops packets with a nearly constant probability. Stability is then investigated for a single TCP connection when this probability is constant. The connection is viewed on a new time scale and modelled as a general state-space Markov chain. Ergodic theory and Foster-Lyapunov drift conditions are employed to show that the Markov chain converges to a steady-state distribution. Stability for near-constant loss probabilities is also considered. The results are extended through the Law of Large Numbers to conclude that constant drop probabilities may cause large TCP networks to converge to a known fixed point. Simulation verifies that RWFD is similarly well behaved, while automatically adapting to network conditions. |
