Delayed Random Walks and Control

Minimize Congestion for Random-Walks in Networks via Local Adaptive Congestion Control

—The routing method of random-walks is robust to the change of network topology. However, congestion occurs easily for random-walks because packets usually take a long trip in the networks to arrive at their destinations. In this paper, we propose a method to minimize the congestion for random-walks via local adaptive congestion control. The method uses linearprediction to estimate the queue l...

A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS

A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...

Spectral solution of delayed random walks.

We develop a spectral method for computing the probability density function for delayed random walks; for such problems, the method is exact to machine precision and faster than existing approaches. In conjunction with a step function approximation and the weak Euler-Maruyama discretization, the spectral method can be applied to nonlinear stochastic delay differential equations (SDDE). In essen...

Delay estimation from noisy time series

We propose here a method to estimate a delay from a time series taking advantage of analysis of random walks with delay. This method is applicable to a time series coming out of a system which is or can be approximated as a linear feedback system with delay and noise. We successfully test the method with a time series generated by discrete Langevin equation with delay. Estimation of delay from ...

Delayed random walks.