Origin-Destination (O-D) matrices are required in order to model traffic routing behavior in networks. Direct techniques for collecting O-D information from home and roadside interviews have historically been utilized to estimate O-D tables. However, these techniques are not only very costly, labor intensive, and disruptive to trip makers, but traditionally also do not capture traffic peaking behavior, which is often required for traffic operational purposes. Consequently, more cost-effective indirect or synthetic O-D estimation techniques have been developed, and continue to be developed. They utilize readily available traffic volume counts to estimate the most likely O-D tables that may have generated the observed link counts. This thesis describes the basic formulations that have been proposed to formulate and solve the static O-D problem synthetically using link flow observations based on Maximum Entropy techniques. As is the case with many mathematical solutions to engineering problems, a number of simplifying assumptions have been made in order to solve the synthetic O-D problem. Unfortunately, the descriptions of these simplifying assumptions are often not fully described in the literature, and in some cases, these assumptions are not mentioned at all. Furthermore, the literature fails to systematically demonstrate what impact these assumptions have on the final O-D table estimate. Therefore, this thesis utilizes simple hypothetical networks to; 1. Demonstrate and compare the two main types of synthetic O-D formulations, namely the trip and volume based formulations. 2. Track the O-D estimation procedure from its initial formulation to its final formulation, demonstrating all significant assumptions that have been made and the implications of these assumptions on the final solution. 3. Demonstrate to what extent the final O-D estimation formulation remains valid when these assumptions are invoked. 4. Test the applicability of some packages which implement the various formulations and solution techniques that are available. / Master of Science

O objetivo deste trabalho é testar um modelo de distribuição de viagens do tipo gravitacional para a calibração de matrizes origem/destino (O/D) em linhas de transporte público por ônibus a partir de dados de pesquisa de contagem de embarque/desembarque (E/D). A metodologia proposta possibilita a obtenção de matrizes O/D de forma rápida e barata, pois combina um método de pesquisa simples e de baixo custo (pesquisa de contagem de usuários) com um modelo de distribuição de viagens. O modelo associa a cada ponto de origem um valor de parâmetro. A utilização de um valor de parâmetro associado a cada origem busca neste caso reproduzir o custo médio de distribuição de viagens de uma origem em relação aos seus diferentes destinos. O modelo incorpora ainda como restrição a probabilidade de um passageiro desembarcar no ponto seguinte ao seu ponto de embarque. Os dados de pesquisa foram cedidos pelo Departamento de Transportes da Universidade Federal do Paraná. O teste de desempenho do modelo foi realizado através da comparação entre matrizes O/D observadas e simuladas para as cidades de Curitiba e Paranaguá. / The aim of this work is to test a gravity model for trip distribution designed to estimate bus routes origin/destination (O/D) matrices based on boarding and alighting data. The proposed method combines a simple and low-cost survey method (on/off passenger counting) with a mathematical model for trip distribution, which enables the estimation of an O/D matrix in a fast and inexpensive manner. The model assumption that each origin point is associated to a parameter value tries to reproduce the average costs of the actual trip distribution from each origin to every single destination along the bus route. The model brings also as a built-in restriction an expected (usually low) probability of passengers getting off the vehicle in the bus stop following the boarding point. The survey data used in this work have been collected by researchers of the Transportation Department at the Federal University of Paraná. The model performance has been tested by the comparison of observed and simulated O/D matrices in the cities of Curitiba and Paranaguá. The results found in most of the simulations showed that for an estimated trip frequencies did not statistically differ from the actual values for a required level of significance.

O objetivo deste trabalho é testar um modelo de distribuição de viagens do tipo gravitacional para a calibração de matrizes origem/destino (O/D) em linhas de transporte público por ônibus a partir de dados de pesquisa de contagem de embarque/desembarque (E/D). A metodologia proposta possibilita a obtenção de matrizes O/D de forma rápida e barata, pois combina um método de pesquisa simples e de baixo custo (pesquisa de contagem de usuários) com um modelo de distribuição de viagens. O modelo associa a cada ponto de origem um valor de parâmetro. A utilização de um valor de parâmetro associado a cada origem busca neste caso reproduzir o custo médio de distribuição de viagens de uma origem em relação aos seus diferentes destinos. O modelo incorpora ainda como restrição a probabilidade de um passageiro desembarcar no ponto seguinte ao seu ponto de embarque. Os dados de pesquisa foram cedidos pelo Departamento de Transportes da Universidade Federal do Paraná. O teste de desempenho do modelo foi realizado através da comparação entre matrizes O/D observadas e simuladas para as cidades de Curitiba e Paranaguá. / The aim of this work is to test a gravity model for trip distribution designed to estimate bus routes origin/destination (O/D) matrices based on boarding and alighting data. The proposed method combines a simple and low-cost survey method (on/off passenger counting) with a mathematical model for trip distribution, which enables the estimation of an O/D matrix in a fast and inexpensive manner. The model assumption that each origin point is associated to a parameter value tries to reproduce the average costs of the actual trip distribution from each origin to every single destination along the bus route. The model brings also as a built-in restriction an expected (usually low) probability of passengers getting off the vehicle in the bus stop following the boarding point. The survey data used in this work have been collected by researchers of the Transportation Department at the Federal University of Paraná. The model performance has been tested by the comparison of observed and simulated O/D matrices in the cities of Curitiba and Paranaguá. The results found in most of the simulations showed that for an estimated trip frequencies did not statistically differ from the actual values for a required level of significance.

This dissertation aims to improve the performance of existing assignment-based dynamic origin-destination (O-D) matrix estimation models to successfully apply Intelligent Transportation Systems (ITS) strategies for the purposes of traffic congestion relief and dynamic traffic assignment (DTA) in transportation network modeling. The methodology framework has two advantages over the existing assignment-based dynamic O-D matrix estimation models. First, it combines an initial O-D estimation model into the estimation process to provide a high confidence level of initial input for the dynamic O-D estimation model, which has the potential to improve the final estimation results and reduce the associated computation time. Second, the proposed methodology framework can automatically convert traffic volume deviation to traffic density deviation in the objective function under congested traffic conditions. Traffic density is a better indicator for traffic demand than traffic volume under congested traffic condition, thus the conversion can contribute to improving the estimation performance. The proposed method indicates a better performance than a typical assignment-based estimation model (Zhou et al., 2003) in several case studies. In the case study for I-95 in Miami-Dade County, Florida, the proposed method produces a good result in seven iterations, with a root mean square percentage error (RMSPE) of 0.010 for traffic volume and a RMSPE of 0.283 for speed. In contrast, Zhou’s model requires 50 iterations to obtain a RMSPE of 0.023 for volume and a RMSPE of 0.285 for speed. In the case study for Jacksonville, Florida, the proposed method reaches a convergent solution in 16 iterations with a RMSPE of 0.045 for volume and a RMSPE of 0.110 for speed, while Zhou’s model needs 10 iterations to obtain the best solution, with a RMSPE of 0.168 for volume and a RMSPE of 0.179 for speed. The successful application of the proposed methodology framework to real road networks demonstrates its ability to provide results both with satisfactory accuracy and within a reasonable time, thus establishing its potential usefulness to support dynamic traffic assignment modeling, ITS systems, and other strategies.

Neste trabalho é proposto um método de carregamento incremental dos fluxos veiculares para a estimação de matriz O-D sintética. A principal motivação para o desenvolvimento deste trabalho está na complexidade dos métodos de estimação de matriz sintética pelo método iterativo, que tem conduzido a resultados não satisfatórios. O método de carregamento incremental, ora proposto neste trabalho, pode ser definido como o inverso do método de alocação incremental de viagens aos arcos de uma rede viária. A matriz O-D obtida com este método é o resultado da soma sucessiva das sub-matrizes estimadas através das parcelas dos fluxos observados nos arcos da rede. Este método pode ser aplicado em qualquer tipo de rede viária: congestionada ou não congestionada e com ou sem continuidade de fluxo. Para verificação do desempenho do método foram realizados testes experimentais, nos quais os resultados obtidos foram comparados com os valores observados. O desempenho do método incremental não se mostrou satisfatório. Assim, com o intuito de verificar a sua utilidade como um método alternativo os mesmos dados foram processados através de dois métodos iterativos. Os resultados mostraram que os erros são ainda maiores do que os obtidos pelo método proposto. A principal conclusão deste trabalho é que o método incremental pode ser usado como uma alternativa aos métodos iterativos. / A synthetic O-D matrix estimation method, based on incremental loading of traffic flow, was proposed in this work. This research was motivated because of the complexity of the iterative methods for synthetic matrix estimation that might produce bias accumulation in the results. The referred incremental loading method could be defined as the inverse of the incremental assignment method for trips to links of a traffic network. The O-D matrix is gathered by successively summing the sub-matrices obtained from parts of the traffic flow counted on the links of the traffic network. This method could be applied to any traffic networks: congested or uncongested and with or without volumetric continuity. As a part of verification proceeding, several experimental tests were carried out to evaluate the method performance. In these tests the estimated results were compared with the real values. These results show that the incremental loading method performance was not satisfactory. Thus, aiming to test the utility of the incremental method, a second round of experimental tests was conducted to evaluate two iterative methods. In these second round tests, the results show that theses methods performance was worse those of the incremental method. The main conclusion of this work is that the incremental loading method for synthetic matrices estimation could be used as an alternative to the iterative methods.

Neste trabalho é proposto um método de carregamento incremental dos fluxos veiculares para a estimação de matriz O-D sintética. A principal motivação para o desenvolvimento deste trabalho está na complexidade dos métodos de estimação de matriz sintética pelo método iterativo, que tem conduzido a resultados não satisfatórios. O método de carregamento incremental, ora proposto neste trabalho, pode ser definido como o inverso do método de alocação incremental de viagens aos arcos de uma rede viária. A matriz O-D obtida com este método é o resultado da soma sucessiva das sub-matrizes estimadas através das parcelas dos fluxos observados nos arcos da rede. Este método pode ser aplicado em qualquer tipo de rede viária: congestionada ou não congestionada e com ou sem continuidade de fluxo. Para verificação do desempenho do método foram realizados testes experimentais, nos quais os resultados obtidos foram comparados com os valores observados. O desempenho do método incremental não se mostrou satisfatório. Assim, com o intuito de verificar a sua utilidade como um método alternativo os mesmos dados foram processados através de dois métodos iterativos. Os resultados mostraram que os erros são ainda maiores do que os obtidos pelo método proposto. A principal conclusão deste trabalho é que o método incremental pode ser usado como uma alternativa aos métodos iterativos. / A synthetic O-D matrix estimation method, based on incremental loading of traffic flow, was proposed in this work. This research was motivated because of the complexity of the iterative methods for synthetic matrix estimation that might produce bias accumulation in the results. The referred incremental loading method could be defined as the inverse of the incremental assignment method for trips to links of a traffic network. The O-D matrix is gathered by successively summing the sub-matrices obtained from parts of the traffic flow counted on the links of the traffic network. This method could be applied to any traffic networks: congested or uncongested and with or without volumetric continuity. As a part of verification proceeding, several experimental tests were carried out to evaluate the method performance. In these tests the estimated results were compared with the real values. These results show that the incremental loading method performance was not satisfactory. Thus, aiming to test the utility of the incremental method, a second round of experimental tests was conducted to evaluate two iterative methods. In these second round tests, the results show that theses methods performance was worse those of the incremental method. The main conclusion of this work is that the incremental loading method for synthetic matrices estimation could be used as an alternative to the iterative methods.

A pesquisa relatada nesta dissertação procura demonstrar como um modelo microscópico de simulação pode ser usado para produzir dados para a quantificação de medidas de desempenho relacionadas ao transporte sustentável, de tal forma que seja possível incorporar a contribuição individual de cada veículo que viaja pela rede em cada medida de desempenho utilizada. Para tanto, é apresentado um estudo de caso no corredor Anhangüera-Bandeirantes, entre São Paulo e Jundiaí, onde foram propostas quatro estratégias operacionais hipotéticas para ilustrar como o índice de sustentabilidade pode ser utilizado na tomada de decisões na área de transportes. O modelo de simulação de tráfego utilizado foi o Integration que teve seus parâmetros de entrada recalibrados a partir dos fluxos obtidos dos laços indutivos instalados ao longo do corredor estudado. As matrizes O/D utilizadas nas simulações foram estimadas através do QueensOD e as medidas de desempenho constituintes do índice de sustentabilidade proposto foram : a taxa de viagem, o consumo de combustível e as emissões de HC, CO e \'NO IND. X\'. / The objectives of the research reported in this masters dissertation was to demonstrate how a microsimulation model outputs can be used to quantify performance measures related to sustainable transportation, in a way such that each individual vehicle contribution is accounted for in the calculation of the performance measures. A case study, focusing the São Paulo to Jundiaí segment of the Anhanguera-Bandeirantes highway corridor, was used to demonstrate the application of the proposed approach. Four hypothetical operational strategies were compared to illustrate how the proposed sustainability index might be used in decision making. The Integration model was used to simulate the highway corridor. The microsimulation model was calibrated using data from the inductive loops installed along the studied section and the synthetic O/D matrices were estimated by means of the QueensOD model, from traffic counts. The sustainability index used included the following performance measures : travel rate, fuel consumption and HC, CO e \'NO IND. X\' emissions.

A pesquisa relatada nesta dissertação procura demonstrar como um modelo microscópico de simulação pode ser usado para produzir dados para a quantificação de medidas de desempenho relacionadas ao transporte sustentável, de tal forma que seja possível incorporar a contribuição individual de cada veículo que viaja pela rede em cada medida de desempenho utilizada. Para tanto, é apresentado um estudo de caso no corredor Anhangüera-Bandeirantes, entre São Paulo e Jundiaí, onde foram propostas quatro estratégias operacionais hipotéticas para ilustrar como o índice de sustentabilidade pode ser utilizado na tomada de decisões na área de transportes. O modelo de simulação de tráfego utilizado foi o Integration que teve seus parâmetros de entrada recalibrados a partir dos fluxos obtidos dos laços indutivos instalados ao longo do corredor estudado. As matrizes O/D utilizadas nas simulações foram estimadas através do QueensOD e as medidas de desempenho constituintes do índice de sustentabilidade proposto foram : a taxa de viagem, o consumo de combustível e as emissões de HC, CO e \'NO IND. X\'. / The objectives of the research reported in this masters dissertation was to demonstrate how a microsimulation model outputs can be used to quantify performance measures related to sustainable transportation, in a way such that each individual vehicle contribution is accounted for in the calculation of the performance measures. A case study, focusing the São Paulo to Jundiaí segment of the Anhanguera-Bandeirantes highway corridor, was used to demonstrate the application of the proposed approach. Four hypothetical operational strategies were compared to illustrate how the proposed sustainability index might be used in decision making. The Integration model was used to simulate the highway corridor. The microsimulation model was calibrated using data from the inductive loops installed along the studied section and the synthetic O/D matrices were estimated by means of the QueensOD model, from traffic counts. The sustainability index used included the following performance measures : travel rate, fuel consumption and HC, CO e \'NO IND. X\' emissions.

The conventional methods of determining the Origin-Destination (O-D) trip tables involve elaborate surveys, such as home interviews, requiring considerable time, manpower and funds. To overcome this drawback, a number of theoretical models that synthesize O-D trip tables from link volume data have been developed in the past. The focus of this research was on two of these models, namely, The Highway Emulator (THE) and the Linear Programming (LP) models. These models use target/seed tables for guiding the modeled trip tables. In an earlier research effort conducted by Virginia Tech Center for Transportation Research, potential was noted for enhancing these models' performances by using a superior target/seed table. This research study exploits the readily available socio-economic/census data and link volume information and proposes a methodology for obtaining improved target/seed tables, by performing the trip generation and trip distribution steps. This table was provided as target to THE and LP models, and their performances evaluated using Pulaski town as case study. In addition to measuring the closeness of the output tables to surveyed tables and their capability to replicate observed volumes, their improvements over the case when a structural table is used as target was also studied. Tests showed that the use of the superior target/seed table significantly improved the performance of the LP model. However, for THE, mixed trends are seen in terms of different measures of closeness. The sensitivity of the user parameter to place certain degree of belief on the target/seed table for LP model was also analyzed. / Master of Science

We have considered the bilevel programming problem in the case where the lower-level problem admits more than one optimal solution. It is well-known in the literature that in such a situation, the problem is ill-posed from the view point of scalar objective optimization. Thus the optimistic and pessimistic approaches have been suggested earlier in the literature to deal with it in this case. In the thesis, we have developed a unified approach to derive necessary optimality conditions for both the optimistic and pessimistic bilevel programs, which is based on advanced tools from variational analysis. We have obtained various constraint qualifications and stationarity conditions depending on some constructive representations of the solution set-valued mapping of the follower’s problem. In the auxiliary developments, we have provided rules for the generalized differentiation and robust Lipschitzian properties for the lower-level solution setvalued map, which are of a fundamental interest for other areas of nonlinear and nonsmooth optimization. Some of the results of the aforementioned theory have then been applied to derive stationarity conditions for some well-known transportation problems having the bilevel structure.