Principal Investigator and Institution
Ronald T. Eguchi, ImageCat, Inc.
Objective
The objectives of Task B14 are to improve the transportation network
analysis module for REDARS by addressing several model deficiencies
identified during the evaluation/validation effort of Task B11, and to
enhance the overall usability of REDARS. The primary findings from Task
B11 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 postearthquake travel demands.
Approach
Research on this task will be conducted via three subtasks, as follows:
Subtask 1  PostEarthquake Traffic Demand Modeling A
user equilibrium (UE) model with fixed demands would highly overestimate
systemwide 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 postearthquake 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) longterm 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 x^{2} 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
dualsimplex 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 dualsimplex algorithm requires ingeniously
designed data storage to allow tree information to be updated easily.
Without efficient data storage, we cannot guarantee that the dualsimplex
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
dualsimplex 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
standalone 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
Multicriteria 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 nonlinear
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 roundoff
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 roundoff 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
