Pilar Jiménez

The Observability Problem in Traffic Network Models

This paper examines the issue of observability of traffic networks, understanding as such the problem of identifying which is the subset of OD-pair and link flows that can be calculated based on a subset of observed OD-pair and link flows and related problems. Two algebraic methods for solving observability problems are given, one global approach based on null-spaces and a step by step procedure allowing updating the information once each item of information (OD-pair or link flow) becomes available. In particular, 7 different observability problems are stated and solved using the proposed methods, illustrated by their application to the Nguyen-Dupuis network problem. Results show that the proposed methods provide useful information on which OD-pair or link flows are informative on other OD-pair and link flows, and that the methods are applicable to large networks.

The Observability Problem in Traffic Models: Algebraic and Topological Methods

This paper deals with the problem of observability of traffic networks, understanding as such the problem of identifying which is the subset of the origin-destination (OD)-pair and link flows that can be calculated based on a subset of observed OD-pair and link flows, and related problems. A modified topological version of an existing algebraic method for solving observability problems is given. The method is based on a step-by-step procedure, allowing us to update the information once each item of information (OD-pair or link flow) becomes available. In particular, three different observability problems are stated and solved using the proposed methodology, which is illustrated by its application to the Nguyen-Dupuis network and compared with the algebraic version. The topological version is much faster, uses much less memory, and presents no rounding errors or zero test problems but identifies fewer observable flows.

Stochastic Demand Dynamic Traffic Models Using Generalized Beta-Gaussian Bayesian Networks

A stochastic demand dynamic traffic model is presented to predict some traffic variables, such as link travel times, link flows, or link densities, and their time evolution in real networks. The model considers that the variables are generalized beta variables such that when they are marginally transformed to standard normal, they become multivariate normal. This gives sufficient degrees of freedom to reproduce (approximate) the considered variables at a discrete set of time-location pairs. Two options to learn the parameters of the model are provided-one based on previous observations of the same variables and one based on simulated data using existing dynamic models. The model is able to provide a point estimate, a confidence interval, or the density of the variable being predicted. To this end, a closed formula for the conditional future variable values (link travel times or flows), given the available past variable information, is provided. Since only local information is relevant to short-term link flow predictions, the model is applicable to very large networks. The following three examples of application are given: (1) the Nguyen-Dupuis network; (2) the Ciudad Real network; and (3) the Vermont state network. The resulting traffic predictions seem to be promising for real traffic networks and can be done in real time.

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%.

Link Flow Estimation in Traffic Networks on the Basis of Link Flow Observations

Given a traffic network, the problem of identifying the smallest subset of links on which to locate sensors that allow the exact estimation of a given subset of links flows is dealt with, and methods for solving this partial link-observability problem are given. As sources of information, the authors consider 2 separate types of link sensors: counters and scanners. The first type leads to a method, which is an alternative to the previous method of Hu, Peeta, and Chu. First, the authors show how the previous method can be directly used for solving the partial observability problem. Next, the authors present a simple alternative algorithm, based on the pivoting strategy, that can include information about route and Origin-Destination (OD) flows observability. The observability problem based on scanners leads to a more difficult problem but supplies much more information about traffic flows. The authors give 2 simple algorithms for solving this problem in this case. The first algorithm allows checking that a given subset of links supplies the required information to estimate the flows in the selected subset of links, and provides information about route and OD observability. The second, which is a random algorithm, permits reducing the number of links of an initial subset of scanned links that solves the problem, and when a further reduction is not possible, modifies the initial set of scanning links for a new trial randomly. The proposed methods are illustrated using the parallel highway network of Hu, Peeta, and Chu. Last, the authors apply methods to two examples of applications—the Nguyen-Dupuis and the real Cuenca network—and provide some conclusions.

A FIFO Rule Consistent Model for the Continuous Dynamic Network Loading Problem

This paper presents a first-in-first-out (FIFO) rule consistent model for the continuous dynamic network loading problem. The model calculates the link travel time functions at a basic finite set of equally spaced times that are used to interpolate a monotone spline for all the other times. The model assumes a nonlinear link travel time function of the link volumes, but some corrections are made to satisfy the FIFO rule at the basic set. Furthermore, the use of monotone cubic splines preserving monotonicity guarantees that the FIFO rule is satisfied at all points. The model consists of five units: 1) a path origin flow wave definition unit; 2) a path wave propagation unit; 3) a congestion analysis unit; 4) a network flow propagation unit; and 5) an inference engine unit. The path flow intensity wave, which is the basic information, is modeled as a linear combination of basic waves. Next, the individual path waves are propagated throughout the paths by using a conservation equation that stretches or enlarges the wave lengths and increases or reduces the wave heights, depending on the degree of congestion at different links. Then, the individual path waves are combined together to generate the link and node waves. Finally, the inference engine unit combines all information items to make them compatible in times and locations using the aforementioned iterative method until convergence. The method is illustrated by some examples. The results seem to reproduce the observed trends closely. The required CPU times oscillated between seconds and a few minutes.