Seismic Vulnerability of the Highway System

Task B1-4: Transportation Model Improvements for REDARS

Subject Area: Loss Estimation Methodologies
Research Year 3

Principal Investigator and Institution

Ronald T. Eguchi, ImageCat, Inc.


The objectives of Task B1-4 are to improve the transportation network analysis module for REDARS by addressing several model deficiencies identified during the evaluation/validation effort of Task B1-1, and to enhance the overall usability of REDARS. The primary findings from Task B1-1 identified a number of technical deficiencies associated with the current modeling assumptions in REDARS. In general, the proposed improvements will help to better match actual earthquake experience data, particularly in modeling post-earthquake travel demands.


Research on this task will be conducted via three subtasks, as follows:

Subtask 1 - Post-Earthquake Traffic Demand Modeling  A user equilibrium (UE) model with fixed demands would highly overestimate system-wide travel costs because the model does not account for changes in demand that occur after the earthquake. Among the reasons for these demand changes are that highway capacity is reduced because of earthquake damage, thus creating an additional impedance on traffic and reducing the level of service at which traffic flows; and the urban activity system may have been affected by the earthquake, thus eliminating the demand for trips to or from some locations. Because these conditions have a significant impact on the modeling of post-earthquake traffic flows, new models that account for trip reduction due to the above conditions must be developed for the next version of REDARS.

Modeling changes in travel (e.g., trip reductions) will be a challenging task because there is currently no complete theory to explain travel demand following a major network disruption. One of promising methods that has emerged in recent years is the "Variable Demand Model." The standard UE modeling exercise holds total demand constant and predicts routes travelers will use and the level of service that will result. The idea behind the variable demand approach is that the standard perspective can be extended and efficient algorithms can be developed that will search for the simultaneous economic equilibrium between route choice, travel demand, and network capacity. Network capacity defines the supply of transportation services, and congested travel times under equilibrium conditions and is similar to quantifying a price users pay when they choose a route or decide whether to travel at all. If there is an available travel demand function, the UE model can be modified to explain trip changes or reductions by scaling travel times to reductions in network capacity. The development of a variable demand model will require four basic steps: (1) develop the basic form of the demand function; (2) automate the calibration of distance decay coefficients; (3) identify the cost of trips forgone; and (4) long-term management of trip reduction data.

Subtask Technical Challenges - Determining the regression domain for the demand function calibration process should be based on a distribution of travel distance (time). In general, this distribution is a x2 distribution, while the gravity formulation function follows a negative exponential profile. Consolidation of different distributions, and automation of the calibration process will present certain technical challenges.

Subtask Products - Source code for prototype variable demand network model; prototype software module for distance decay coefficient calibration; technical report describing variable demand model and distance decay calibration routine; and user's manual for calibration tool.

Subtask 2 - Improvement of Minimum Path Search Algorithm  Because REDARS incorporates a Minimum Time Path (MTP) search module that is based on the use of the Dijkstra algorithm, a probabilistic assessment of traffic states for multiple earthquakes requires an enormous amount of computer time. Currently, the application of the UE module accounts for approximately 95% of the total running time of REDARS. To reduce this time - without sacrificing any analytical accuracy - the Minimum Path Search Algorithm will be replaced with a more advanced algorithm based on dual-simplex theory. A primal code for this algorithm will be developed and assessed to confirm the expected reductions in running time. The algorithm will be coded and tested for various network types.

Subtask Technical Challenges - A highly complex data structure may pose a challenge. The dual-simplex algorithm requires ingeniously designed data storage to allow tree information to be updated easily. Without efficient data storage, we cannot guarantee that the dual-simplex algorithm will significantly reduce running time. If data storage is inefficient, the MTP tree would require more time to identify which links could be reused, or which parts of the network must be updated. While this dual-simplex algorithm was proposed more than two decades ago, its use has not been widespread due to the difficulty associated with implementation of data structure, particularly in software packages.

Subtask Products - Source code to be incorporated in REDARS; and a stand-alone program that is incorporated into an UE model.

Subtask 3 - Investigation of MAM Matrix Training Scheme   In the current REDARS program, stochastic analyses are performed using a Multi-criteria Associative Memory (MAM) method. This method, as implemented in REDARS, must be improved to allow the training scheme to incorporate reciprocal effects between closed links, and the non-linear nature of the solution to the UE problem. Although MAM was initially developed to prevent the numerical instability of the generalized inverse matrix, the training scheme has been applied to transportation systems in only limited ways. If MAM is to be used for rapid traffic estimation, it must be refined so that it characterizes link traffic volumes more efficiently.

The MAM method has certain advantages over the UE model when it comes to analyzing large numbers of network configurations (system states) simultaneously; namely, lower computation time. However, there are still some development questions that require further study. One important question is the quality or accuracy of the estimate when it deals with traffic volume. To resolve such issues, two possible improvements will be investigated: (1) a study on the training scheme, and (2) a study on the enhancement of nonlinearity.

Subtask Technical Challenges - Implementing an inverse algorithm for a highly dense, and large matrix would be challenging. Because of round-off error, the inverse of the matrix can be numerically unstable, particularly when the matrix is very large . Furthermore, applying exponents to stimulus vectors will make round-off errors more serious. Highly refined numerical analysis techniques may be required to offset this problem.

Subtask Products - Code for new "Systematic Training Case" module; code for new MAM training module; technical report

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