Distributed dynamic stochastic approximation algorithm over time-varying networks

In this paper, a distributed stochastic approximation algorithm is proposed to track the dynamic root of a sum of time-varying regression functions over a network. Each agent updates its estimate by using the local observation, the dynamic information of the global root, and information received from its neighbors. Compared with similar works in optimization area, we allow the observation to be noise-corrupted, and the noise condition is much weaker. Furthermore, instead of the upper bound of the estimate error, we present the asymptotic convergence result of the algorithm. The consensus and convergence of the estimates are established. Finally, the algorithm is applied to a distributed target tracking problem and the numerical example is presented to demonstrate the performance of the algorithm.

Estimation of Path Travel Time Distributions in Stochastic Time-Varying Networks with Correlations

Transportation research has increasingly focused on the modeling of travel time uncertainty in transportation networks. From a user’s perspective, the performance of the network is experienced at the level of a path, and, as such, knowledge of variability of travel times along paths contemplated by the user is necessary. This paper focuses on developing approaches for the estimation of path travel time distributions in stochastic time-varying networks so as to capture generalized correlations between link travel times. Specifically, the goal is to develop methods to estimate path travel time distributions for any path in the networks by synthesizing available trajectory data from various portions of the path, and this paper addresses that problem in a two-fold manner. Firstly, a Monte Carlo simulation (MCS)-based approach is presented for the convolution of time-varying random variables with general correlation structures and distribution shapes. Secondly, a combinatorial data-mining approach is developed, which aims to utilize sparse trajectory data for the estimation of path travel time distributions by implicitly capturing the complex correlation structure in the network travel times. Numerical results indicate that the MCS approach allowing for time-dependence and a time-varying correlation structure outperforms other approaches, and that its performance is robust with respect to different path travel time distributions. Additionally, using the path segmentations from the segment search approach with a MCS approach with time-dependence also produces accurate and robust estimates of the path travel time distributions with the added benefit of shorter computation times.