Stability of adaptive congestion controls in packet networks
Abstract Some congestion controls used in packet networks are static, while others are adaptive, i.e., they respond on the basis of estimated load determined from measurements. Adaptive controls pose a potential stability problem. If the network reacts too strongly to overload, its load level may oscillate widely. In this paper, we examine the effect of offered overload and measurement error on the response of the network. We also study the effect of smoothing measurements. The model requires non-zero time to respond after a measurement of the load is taken. Results include conditions for convergence to a desired load, rate of convergence, and variance of system load as time goes to infinity as a function of system parameters.
We discuss recent findings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties. It is shown that the time dependent density matrix renormalization method can be used successfully to find a stationary solution of Lindblad master equation. Furthermore, for a specific model an exact solution is presented.