In a communication network, point-to-point traffic volumes over time are critical for designing protocols that route information efficiently and for maintaining security, whether at the scale of an internet service provider or within a corporation. While technically feasible, the direct measurement of point-to-point traffic imposes a heavy burden on network performance and is typically not implemented. Instead, indirect aggregate traffic volumes are routinely collected. We consider the problem of estimating point-to-point traffic volumes, x_t, from aggregate traffic volumes, y_t, given information about the network routing protocol encoded in a matrix A. This estimation task can be reformulated as finding the solutions to a sequence of ill-posed linear inverse problems, y_t = A x_t, since the number of origin-destination routes of interest is higher than the number of aggregate measurements available. Here, we introduce a novel multilevel state-space model of aggregate traffic volumes with realistic features. We implement a naive strategy for estimating unobserved point-to-point traffic volumes from indirect measurements of aggregate traffic, based on particle filtering. We then develop a more efficient two-stage inference strategy that relies on model-based regularization: a simple model is used to calibrate regularization parameters that lead to efficient and scalable inference in the multilevel state-space model. We apply our methods to corporate and academic networks, where we show that the proposed inference strategy outperforms existing approaches and scales to larger networks. We also design a simulation study to explore the factors that influence the performance. Our results suggest that model-based regularization may be an efficient strategy for inference in other complex multilevel models.
Applied research related to the type of problems we consider can be traced back to literature on transportation and operations research . There the focus is on estimating a single set of origin-destination traffic volumes, @math , from integer-valued traffic counts over time, @math . The line of research in statistics with application to communication networks is due to who coined the term by extending the approach to positron emission tomography by @cite_1 . In this latter setting, statistical approaches may be able to leverage knowledge about a physical process, explicitly specified by a model, to assist the inference task. In the network tomography setting, in contrast, we can only rely on knowledge about the routing matrix and statistics about traffic time series.
@cite_1
2069069662 2083797062 2083651391 1544613517
The monitoring of a system can yield a set of measurements that can be modeled as a collection of time series. These time series are often sparse, due to missing measurements, and spatiotemporally correlated, meaning that spatially close time series exhibit temporal correlation. The analysis of such time series offers insight into the underlying system and enables prediction of system behavior. While the techniques presented in the paper apply more generally, we consider the case of transportation systems and aim to predict travel cost from GPS tracking data from probe vehicles. Specifically, each road segment has an associated travel-cost time series, which is derived from GPS data. We use spatio-temporal hidden Markov models (STHMM) to model correlations among different traffic time series. We provide algorithms that are able to learn the parameters of an STHMM while contending with the sparsity, spatio-temporal correlation, and heterogeneity of the time series. Using the resulting STHMM, near future travel costs in the transportation network, e.g., travel time or greenhouse gas emissions, can be inferred, enabling a variety of routing services, e.g., eco-routing. Empirical studies with a substantial GPS data set offer insight into the design properties of the proposed framework and algorithms, demonstrating the effectiveness and efficiency of travel cost inferencing. Traffic volume data is already collected and used for a variety of purposes in intelligent transportation system (ITS). However, the collected data might be abnormal due to the problem of outlier data caused by malfunctions in data collection and record systems. To fully analyze and operate the collected data, it is necessary to develop a validate method for addressing the outlier data. Many existing algorithms have studied the problem of outlier recovery based on the time series methods. In this paper, a multiway tensor model is proposed for constructing the traffic volume data based on the intrinsic multilinear correlations, such as day to day and hour to hour. Then, a novel tensor recovery method, called ADMM-TR, is proposed for recovering outlier data of traffic volume data. The proposed method is evaluated on synthetic data and real world traffic volume data. Experimental results demonstrate the practicability, effectiveness, and advantage of the proposed method, especially for the real world traffic volume data. Estimating and predicting traffic situations over time is an essential capability for sophisticated driver assistance systems and autonomous driving. When longer prediction horizons are needed, e.g., in decision making or motion planning, the uncertainty induced by incomplete environment perception and stochastic situation development over time cannot be neglected without sacrificing robustness and safety. Building consistent probabilistic models of drivers interactions with the environment, the road network and other traffic participants poses a complex problem. In this paper, we model the decision making process of drivers by building a hierarchical Dynamic Bayesian Model that describes physical relationships as well as the driver's behaviors and plans. This way, the uncertainties in the process on all abstraction levels can be handled in a mathematically consistent way. As drivers behaviors are difficult to model, we present an approach for learning continuous, non-linear, context-dependent models for the behavior of traffic participants. We propose an Expectation Maximization (EM) approach for learning the models integrated in the DBN from unlabeled observations. Experiments show a significant improvement in estimation and prediction accuracy over standard models which only consider vehicle dynamics. Finally, a novel approach to tactical decision making for autonomous driving is outlined. It is based on a continuous Partially Observable Markov Decision Process (POMDP) that uses the presented model for prediction. In their goal to effectively manage the use of existing infrastructures, intelligent transportation systems require precise forecasting of near-term traffic volumes to feed real-time analytical models and traffic surveillance tools that alert of network links reaching their capacity. This article proposes a new methodological approach for short-term predictions of time series of volume data at isolated cross sections. The originality in the computational modeling stems from the fit of threshold values used in the stationary wavelet-based denoising process applied on the time series, and from the determination of patterns that characterize the evolution of its samples over a fixed prediction horizon. A self-organizing fuzzy neural network is optimized in its configuration parameters for learning and recognition of these patterns. Four real-world data sets from 3 interstate roads are considered for evaluating the performance of the proposed model. A quantitative comparison made with the results obtained by 4 other relevant prediction models shows a favorable outcome.