Aida Calviño

A Markovian-Bayesian Network for Risk Analysis of High Speed and Conventional Railway Lines Integrating Human Errors

The article provides a new Markovian-Bayesian network model to evaluate the probability of accident associated with the circulation of trains along a given high speed or conventional railway line with special consideration to human error. This probability increases as trains pass throughout the different elements encountered along the line. A Bayesian network, made up of a sequence of several connected Bayesian subnetworks, is used. A subnetwork is associated with each element in the line that implies a concentrated risk of accident or produces a change in the drivers attention, such as signals, tunnel, or viaduct entries or exits, etc. Bayesian subnetworks are also used to reproduce segments without signals where some elements add continuous risks, such as rolling stock failures, falling materials, slope slides in cuttings and embankments, etc. All subnetworks are connected with the previous one and some of them are multi-connected because some consequences are dependent on previous errors. Because drivers attention plays a crucial role, its degradation with driving time and the changes due to seeing light signals or receiving acoustic signals is taken into consideration. The model updates the drivers attention level and accumulates the probability of accident associated with the different elements encountered along the line. This permits us to generate a continuously increasing risk graph that includes continuous and sudden changes indicating where the main risks appear and whether or not an action must be taken by the infrastructure manager. Sensitivity analysis allows the relevant and irrelevant parameters to be identified avoiding wastes of time and money by concentrating safety improvement actions only on the relevant ones. Finally, some examples are used to illustrate the model. In particular, the case of the Orense-Santiago de Compostela line, where a terrible accident took place in 2013.

On the Probabilistic and Physical Consistency of Traffic Random Variables and Models

Consideration of the existing relations among the different random variables involved in traffic problems is crucial in developing a consistent probability model. The consistency of stochastic traffic models from the points of view of probability and statistics and also from a dimensional analysis perspective are presented in this paper. The authors analyze and discuss the conditions for a model to be consistent from two different points of view: probabilistic and physical (dimensional analysis). Probabilistic leads to the concept of stability in general and reproductivity in particular because, for example, origin-destination (OD) and link flows are the sum of route flows and route travel times are the sum of link travel times. This implies stability with respect to sums (reproductivity). Normal models are justified because when the number of summands increases the averages approach the normal distribution. Similarly, stability with respect to minimum or maximum operations arises in practice. From the dimensional analysis point of view, some models are demonstrated not to be convenient. In particular, it is shown that some families of distributions are valid only for dimensionless variables. These problems are discussed and some proposed models in the literature are analyzed from these two points of view. When analytical consistency cannot be achieved, a possible alternative is the Monte Carlo simulation that permits satisfying the compatibilities easily.

A State-of-the-Art Review of the Sensor Location, Flow Observability, Estimation, and Prediction Problems in Traffic Networks

A state-of-the-art review of flow observability, estimation, and prediction problems in traffic networks is performed. Since mathematical optimization provides a general framework for all of them, an integrated approach is used to perform the analysis of these problems and consider them as different optimization problems whose data, variables, constraints, and objective functions are the main elements that characterize the problems proposed by different authors. For example, counted, scanned or “a priori” data are the most common data sources; conservation laws, flow nonnegativity, link capacity, flow definition, observation, flow propagation, and specific model requirements form the most common constraints; and least squares, likelihood, possible relative error, mean absolute relative error, and so forth constitute the bases for the objective functions or metrics. The high number of possible combinations of these elements justifies the existence of a wide collection of methods for analyzing static and dynamic situations.

Deriving the Upper Bound of the Number of Sensors Required to Know All Link Flows in a Traffic Network

It is demonstrated that the minimum number of sensors required to know all link flows in a traffic network can be determined only if path information is available. However, not all paths need to be enumerated but, at most, a small subset defining the rank rw of the link-path incidence matrix W. If this rank for a reduced subset of paths is already m - n, where m and n are the number of links and noncentroid nodes, respectively, we can conclude that m - n sensors are sufficient. It is also shown that the formulas providing the dependent link flows in terms of the independent link flows can be obtained by the node-based or path-based approaches with the same results only when rw = m - n. Finally, an algorithm to obtain the small subsets of linearly independent path vectors is given. The methods are shown by a parallel network example and the Ciudad Real and Cuenca networks, for which the savings in link counts with respect to the m - n bound are larger than 16%. The corresponding savings in path enumeration are larger than 80%.

A hierarchical optimization problem: Estimating traffic flow using Gamma random variables in a Bayesian context

In this paper a hierarchical optimization problem generated by a Bayesian method to estimate origin-destination matrices, based on Gamma models, is given. The problem can be considered as a system of equations in which three of them are optimization problems: (1) a Wardrop minimum variance (WMV) assignment model, which is used to derive the route choice probabilities, (2) a least squares problem, used to obtain the OD sample data, and (3) a maximum likelihood problem to estimate the posterior modes. A multi-level iterative approach is proposed to solve the multi-objective problem that converges in a few iterations. Finally, two examples of applications are used to illustrate the proposed methods and procedures, a simple and the medium size Ciudad Real networks. A comparison with existing techniques, which provide similar flows, seems to validate the proposed methods.

A percentile system optimization approach with and without path enumeration

In this paper we deal with the travel time reliability PUE (probabilistic user equilibrium) problem studied by Lo et al. (2006) 12] and Nie (2011) 15] and we propose an alternative model that assumes a location-scale family for the path travel times, whose means and variances are evaluated in terms of link travel times. This avoids the use of the central limit theorem and convolutions providing a flexible and simple alternative. Contrary to the most existing models that require path enumeration or an iterative method to add paths sequentially, we present a percentile system optimization in its two versions: with and without path enumeration. Two examples of applications, one of them real, are used to illustrate the power of the proposed method. The cpu times required to solve the problem seem reasonable. In addition, we answer an open question raised by Nie (2011) 15] about the permutability of percentiles and partial derivatives of route travel times with respect to route flows. A family of counterexamples is given to demonstrate that the two operations: (a) obtain percentiles and (b) partial derivation of route travel times do not commute. Finally, to reproduce the trial-and-error sequence followed by users when selecting paths, we also present an algorithm that simulates this iterative process and shows that the final long-term user behavior coincides with PUE (probabilistic user equilibrium) problem resulting from some existing models.

A Model for Continuous Dynamic Network Loading Problem with Different Overtaking Class Users

This article presents a model for solving the continuous loading network problem when different class users interact in the traffic network so that overtaking among different class users is permitted but the FIFO rule is satisfied for the same class users. The model calculates the link travel time functions at a basic finite set of equally spaced times, which are used to interpolate a monotone spline for all other times in order to preserve monotonicity and guarantee that the FIFO rule is satisfied at all points for the same class users. The model assumes nonlinear link travel time functions of the link volumes including those ahead of the link a being considered, takes into account that different class functions must be asymptotically coincident for high congestions, and considers link physical queues. The path origin demands are reproduced as linear combinations of density functions and the conservation laws are used to determine the path flow wave evolution throughout the network. Different path flow waves are mixed together and a congestion equation is used to determine the link travel times. Finally, all information is combined to make it compatible in times and locations using an iterative method until convergence. The method is illustrated by some examples of illustrative and real networks. The results seem to reproduce the observed trends closely. The resulting required CPU times are reasonable so that the method seems to be applicable to real networks.

A Multiclass User Equilibrium Model Considering Overtaking Across Classes

In this paper, we deal with the traffic assignment problem solving a multiclass equilibrium problem. In particular, we focus our analysis on when the overtaking of vehicles is permitted. A new family of link travel time functions is presented, which allows us to reproduce the same asymptotic congestion behavior of several overtaking classes to mimic the fact that high congestion impedes overtaking and that all classes must have identical link travel times. This family is generated based on local linear convex combinations of travel time Bureau of Public Roads (BPR) functions. A nonlinear complementary problem (NCP), which does not require path enumeration, is used to solve the user-optimal traffic assignment. An example is used to show the proposed methods and techniques. In particular, a case in which cars and motorcycles share the network is analyzed under congested and uncongested conditions.

Coherent and Compatible Statistical Models in Structural Analysis

Intending Modelling problems in structural analysis requires of a statistical approach that allows to take into account the random nature of the variables as well as the uncertainties involved in the problem being analyzed. However neither all statistical models are valid nor all assumptions are mathematically or physically reasonable. The aim of this paper is twofold: (a) to explain how to build statistical models with mathematical and physical coherence, and (b) to describe the most common mistakes made when building or selecting mathematical and statistical models. We provide some interesting tools to carry out this important task and present some examples that show the inconveniences and consequences derived from an incorrectly established model.

Two Applications of Statistics to Traffic Models

Two statistical applications for estimation and prediction of flows in traffic networks are presented. In the first, the number of route users are assumed to be independent α-shifted gamma Γ(θ, λ0) random variables denoted H(α, θ, λ0), with common λ0. As a consequence, the link, OD (origin-destination) and node flows are also H(α, θ, λ0) variables. We assume that the main source of information is plate scanning, which permits us to identify, totally or partially, the vehicle route, OD and link flows by scanning their corresponding plate numbers at an adequately selected subset of links. A Bayesian approach using conjugate families is proposed that allows us to estimate different traffic flows. In the second application, a stochastic demand dynamic traffic model to predict some traffic variables and their time evolution in real networks is presented. The Bayesian network model considers that the variables are generalized Beta variables such that when marginally transformed to standard normal become multivariate normal. The model is able to provide a point estimate, a confidence interval or the density of the variable being predicted. Finally, the models are illustrated by their application to the Nguyen Dupuis network and the Vermont-State example. The resulting traffic predictions seem to be promising for real traffic networks and can be done in real time.