Heuristic for the Bilevel Origin-Destination Matrix Estimation Problem

Abstract In this paper we consider the estimation of an origin-destination (OD) matrix, given a target OD-matrix and traffic counts on a subset of the links in the network. We use a general nonlinear bilevel minimization formulation of the problem, where the lower level problem is to assign a given OD-matrix onto the network according to the user equilibrium principle. After reformulating the problem to a single level problem, the objective function includes implicitly given link flow variables, corresponding to the given OD-matrix. We propose a descent heuristic to solve the problem, which is an adaptation of the wellknown projected gradient method. In order to compute a search direction we have to approximate the Jacobian matrix representing the derivatives of the link flows with respect to a change in the OD-flows, and we propose to do this by solving a set of quadratic programs with linear constraints only. If the objective function is differentiable at the current point, the Jacobian is exact and we obtain a gradient. Numerical experiments are presented which indicate that the solution approach can be applied in practice to medium to large size networks

Aggregate calibration of microscopic traffic simulation models

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2004.Includes bibliographical references (p. 97-101).The problem of calibration of microscopic simulation models with aggregate data has received significant attention in recent years. But day-to-day variability in inputs such as travel demand has not been considered. In this thesis, a general formulation has been proposed for the problem in the presence of multiple days of data. The formulation considers the day-to-day variability in all the inputs to the simulation model. It has then been formulated using Generalized least squares (GLS) approach. The solution methodology for this problem has been proposed and the feasibility of this methodology has been shown with the help of two case studies. One of them is with an experimental network and the other is with network from Southampton, UK. The results indicate that estimation of day-to-day OD flows is feasible. They also reinforce the importance of having good apriori information on the OD flows and locating the sensors so as to obtain maximum information.by Bhanu Prasad Mahanti.S.M

Modeling temporal variations in travel demand for intelligent transportation systems

The imbalance between demand and supply on transportation networks, especially during peak periods, leads to significant level of congestion. Potential solutions to alleviate congestion problems include enhancing system capacity and effective utilization of available capacity--i.e., traffic demand management. Intelligent transportation system (ITS) initiatives such as travel demand management systems (TDMS) and traveler information systems (TIS) refer to demand management as an objective. The success of these initiatives rely heavily on an ability to accurately estimate the temporal variations in travel demand in near real-time. The focus of this dissertation is on developing a methodology for estimating temporal variations in travel demand in urban areas; A significant portion of daily congestion on urban transportation networks occur during peak periods. A majority of trips during peak periods are work trips. The peak study period is divided into several time slices to facilitate simulation and modeling. A methodology is developed to estimate origin-destination (O-D) trip tables for each time slice. Trip attractions during each time slice, for each traffic analysis zone (TAZ), are estimated using pertinent characteristics of the TAZ. The O-D trip tables for each time slice are estimated as a function of trip attractions for the time slice, total trip productions during the peak period and the travel time matrix for the peak period. These O-D trip tables for each time slice and the existing network conditions can be used to assign trips in near real-time; The algorithm is coded using C++ programming language. The model is first tested on various small hypothetical cases with 5 TAZs, 10 TAZs, 15 TAZS and 20 TAZs respectively. The results obtained are as expected. The robustness of the model is tested using the hypothetical case with 10 TAZs. Since, testing and validating the model on large real world networks is important, the model is tested with 1995 data obtained for the Las Vegas valley. The results are consistent with that obtained for the hypothetical cases. The model is tested on Silicon Graphics IP 27 with IRIX version 6.4 as the operating system. For almost all the scenarios, the run time is less than 3 minutes. This strengthens the notion that the model can be implemented in real time

Joint calibration of a microscope traffic simulator and estimation of origin-destination flows

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2002.Includes bibliographical references (p. 103-105).Microscopic Traffic simulators can be effectively used to analyze various transportation strategies (especially ITS related). However, microscopic traffic simulators need to be calibrated in order to yield meaningful results. Calibration is the process of adjusting the model parameters to closely replicate the observed behavior. In this thesis, a module for joint calibration of a microscopic traffic simulator along with estimation of Origin- Destination (OD) flows has been developed. The developed framework takes into account the interactions between the various model parameters and the OD flows. An optimization-based framework has been proposed for the joint calibration of model parameters and estimation of dynamic OD flows. A systematic search approach based on the Box algorithm is adopted for calibration of the parameters. Depending on the problem size, a sequential or a simultaneous OD estimation algorithm is employed. Since the calibration of the parameters depends on the estimated OD flows and vice versa, the proposed framework is iterative. The developed framework has been implemented in MITSIMLab, a microscopic traffic simulation laboratory. Case studies on three networks with varying levels of complexity illustrate the potential of the calibration approach.by Deepak Darda.S.M

Estimation of trip matrices from traffic counts: An equilibrium approach

In urban traffic management and planning, an important problem is how to obtain estimates of origin-destination (O-D) trip matrices using low-cost data such as traffic counts. Although conventional methods using the data from direct surveys can be used to estimate trip matrices, they appear to be inaccurate and expensive. By contrast, the use of traffic counts is attractive, as it is less expensive and more practical. The main objective of the research reported in this thesis is to develop new methods for estimating trip matrices from traffic counts when congestion effects in networks are considered. The problem and existing methods including the sequential solution method used in the ME2 model are reviewed. A new formulation is given for the problem which solves the two sub-problems of entropy maximization and equilibrium traffic assignment simultaneously. It allows modelled link flows to be constrained so as to equal observed ones without link assignment proportions of the trips. A simultaneous solution method is presented for this new formulation. To reduce the considerable computational burden in solving the problem, a heuristic method has been developed which uses a linear approximation fitted by regression to the equilibrium link flows. Extrapolation and perturbation methods have also been used to speed up the solution process. However, the simultaneous solution method appears to be impractical for use in large networks because of the heavy computational demand. As an alternative, an improved sequential solution method is proposed which uses a penalty function method. This method approximates a solution by solving a sequence of problems, while fixed link assignment proportions are used. The performance of the proposed methods has been tested and compared with that of the existing sequential ME2 method using both small example networks and a larger real network. The results show that the simultaneous method works well and that it performs better than the existing sequential method or the improved sequential method. The improved sequential method is also shown to perform closely to the simultaneous one. Some practical implications of the new methods including the robustness of the solutions and the increased computational burden are discussed and they are also compared with those of the sequential solution method. The conclusions from the main findings of the research are drawn and a number of suggestions for further study are given