Asymptotic behavior of flows in networks

Asymptotic Behavior of the Maximum Entropy Routing in Computer Networks

Maximum entropy method has been successfully used for underdetermined systems. Network design problem, with routing and topology subproblems, is an underdetermined system and a good candidate for maximum entropy method application. Wireless ad-hoc networks with rapidly changing topology and link quality, where the speed of recalculation is of crucial importance, have been recently successfully ...

The Burstiness Behavior of Regulated Flows in Networks

In this paper we study the impact of statistical multiplexing on leaky-bucket regulated traffic streams as they pass through the network. In particular we show that the burstiness of a flow is randomized as it transits through the nodes with mean equal to its initial burstiness value at the ingress. We then show that the random burstiness for a single flow converges to a constant equal to the i...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks with Delays

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the R(n)(+)-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-V...

Asymptotic Behavior of Internet Congestion Controllers in a Many-Flows Regime

Congestion controllers for the Internet are typically designed based on deterministic delay differential equation models. In this paper, we consider the case of a single link accessed by many TCP-like congestion-controlled flows, and uncontrolled flows which are modeled as stochastic disturbances. We show that if the number of flows is large and the link capacity is scaled in proportion to the ...