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PANAM 2016. Comité Científico Internacional José Holguín-Veras Rensselaer Polytechnic Institute, USA (Presidente) Helena Cybis Universidad Federal do Rio Grande do Sul, Brasil Víctor Cantillo Universidad del Norte, Colombia Rodrigo Garrido Universidad Diego Portales, Chile Angel Ibeas Universidad de Cantabria, España Juan de Dios Ortúzar Pontificia Universidad Católica de Chile, Chile

Comité Científico Nacional

Angélica Lozano Instituto de Ingeniería, Universidad Nacional Autónoma de México

Francisco Granados Instituto de Ingeniería, Universidad Nacional Autónoma de México Alejandro Guzmán Instituto de Ingeniería, Universidad Nacional Autónoma de México

Ricardo Aceves Facultad de Ingeniería, Universidad Nacional Autónoma de México

Juan Pablo Antún Instituto de Ingeniería, Universidad Nacional Autónoma de México Eduardo Betanzo Facultad de Ingeniería, Universidad Autónoma de Querétaro Rafael Carmona Facultad de Ciencias Económicas y Empresariales, Universidad Anáhuac Norte

Javier García-Gutiérrez Facultad de Ingeniería, Universidad Autónoma del Estado de México María Cristina Gigola Instituto Tecnológico Autónomo de México Gloria Elena Londoño Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México Roberto Magallanes Instituto de Ingeniería, Universidad Nacional Autónoma de México

Alberto Mendoza Coordinación de Seguridad y Operación del Transporte, Instituto Mexicano del Transporte Roger Ríos-Mercado Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Nuevo León Luis Rocha-Chiu División de Ciencias y Artes para el Diseño, Universidad Autónoma Metropolitana Javier Romero-Torres Unidad Académica Profesional Nezahualcoyotl, Universidad Autónoma del Estado de México Esther Segura Facultad de Ingeniería, Universidad Nacional Autónoma de México

1XIX Congreso Panamericano de Ingeniería de Tránsito, Transporte y Logística.

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Comité Organizador Angélica Lozano Instituto de Ingeniería, Universidad Nacional Autónoma de México (Presidenta) Francisco Granados Instituto de Ingeniería, Universidad Nacional Autónoma de México (Secretario Operativo) Alejandro Guzmán Instituto de Ingeniería, Universidad Nacional Autónoma de México (Secretario Ejecutivo)

Sonia Briceño Instituto de Ingeniería, Universidad Nacional Autónoma de México Gustavo Camacho Instituto de Ingeniería, Universidad Nacional Autónoma de México Maribel Miranda Instituto de Ingeniería, Universidad Nacional Autónoma de México

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Prefacio............................................................................................................................Angélica Lozano

Economía y planeación de transporte

Estimación de matrices de viajes usando diagramas de carga........................................Alejandro M. Tudela / Román. Álvaro Toledo / Juan A. Carrasco

The estimative of TTV models to air transportation.......................................................Fernanda David Weber / Ana Margarida Larrañaga Uriate / Luis Afonso dos Santos Senna

VRP en la optimización de rutas.....................................................................................Fredy Sánchez Hernández / Esther Segura Pérez

Factores que afectan la severidad de accidentes urbanos...............................................Carmelo J. Díaz / Víctor Cantillo / Luis Márquez

Elección modal con datos PR-PD...................................................................................Thomas E Guerrero Barbosa / Isabel C. León / Elmar J. Criado

Highway Safety Planning Models...................................................................................Erika C. Jaramillo Giraldo / Bryan Ruiz Cruz / Didier M. Valdés Díaz

Variables de personalidad y la evaluación de un proyeto de transporte.........................Arnoldo Tapia Riffo / Alejandro Tudela Román / Juan Carrasco Montagna

User acceptance of road pricing’s core principles..........................................................José Holguín-Veras / Trilce Encarnación / Carlos A. González-Calderón

Measuring the contribution of transport infrastructure...................................................José F. Baños / Matías Mayor / Pelayo Arbués

Financiamiento del transporte y concesiones privadas

Financial feasibility of pipeline and road modes integration..........................................Miller J.Vargas Gonzaga / Ilton C. Leal Junior / Pitias Teodoro / Vanessa de Almeida Guimarães / Juliana Monteiro Lopes

Rentabilidad de autopistas en México.............................................................................Luis Antonio Rocha Chiu / Antonio Sánchez Soliño / Manuel Rivas Cervera

Opción de abandono en concesiones de autopistas.........................................................Fernando Cabero Colín / Antonio Sánchez Soliño / Antonio L. Lara Galera

2 3XIX Congreso Panamericano de Ingeniería de Tránsito, Transporte y Logística. XIX Congreso Panamericano de Ingeniería de Tránsito, Transporte y Logística.

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Desenvolvimento do Arco Norte Brasileiro: Matriz Rodo-Hidroviária.........................Eliezé Bulhões de Carvalho / Tafarel Carvalho de Gois / Geraldo M. Leite Junqueira / Graziela Moura / Tharcia S. Vasconcelos

Infraestructura de transporte

Impacto infraestructura vial del ambiente.......................................................................Edison F. Velandia Rodríguez

Análise da sinalização aeroportuária através da percepção do usuário..........................Reinaldo Moreira Del Fiaco / Paulo C. Marques da Silva / Paulo R. Vieira de Almeida / Tafarel Carvalho de Gois

Infraestructura vial segura a partir de iRAP...................................................................María G. Saucedo Rojas / Alberto Mendoza Díaz / Jaime G. Pérez Castro

Estudo das patologias de pavimentação..........................................................................Wemerson Rodrigues Caixêta / Jaquelline da Silva Feitoza

Accessibility at airports...................................................................................................Jordana Bulhões Dias / Lílian dos Santos Fontes Pereira Bracarense / Jéssica Monte Neves Carvalho

Methodology to identify aptitude of rail freight terminals.............................................Cristiano Farias Almeida / Luciana Joyce Hamer / Yaeko Yamashita

Evaluación de mezcla drenante con fibra........................................................................Yee Wan Yung Vargas / Jorge Eliécer Córdoba Maquilón / Hugo Alexander Rondón Quintana

Simulation and optimization for the urban transport infraestructure.............................Idalia Flores De La Mota / Esther Segura Pérez

Fricción en el diseño geométrico de vías.......................................................................Luis Alberto Sánchez Muñoz / John Jairo Posada Henao

Ingeniería de tránsito

El tráfico generado por inmuebles...................................................................................Félix Israel Cabrera Vega

Microsimulación flujo vehicular en via rápida...............................................................Daphne Espejel García / José A. Saniger Alba / Gilberto Wenglas Lara / Vanessa V. Espejel García / Alejandro Villalobos

Corredor virtual de motocicletas brasileiro.....................................................................Raquel da Fonseca Holz / Fábio Saraiva da Rocha / Luis Antonio Lindau

Evaluación operacional de carriles de ascenso...............................................................Víctor Gabriel Valencia Alaix / Alfredo García García

Programa para ejecuciones del TAM - IHSDM..............................................................Víctor Gabriel Valencia Alaix / Juan Carlos Calle Rojas

Geração de viagens para empreedimentos hoteleiros.....................................................Henrique Eduardo Araújo Coelho / Rogério Faria D’Avila

Microsimulación de peatones en ambientes universitarios.............................................Félix I. Cabrera Vega / Manuel G. Sabino Gonzales / Gabriel S. Luis Legua Landeo

Logística y transporte de mercancías

Movimentação de multidões em situações emergenciais...............................................João Carlos Souza

Modelagem dos processos de aquisição e transporte em desastres................................Fabiana Santos Lima / Ricardo Villarroel Dávalos / Mirian Buss Gonçalves

Modelación elección portuaria autómatas celulares.......................................................Mabel Leva / Ángel Ibeas / Alejandro León / Rodrigo A. Garrido

Cenários de transporte de commodity agrícola...............................................................Tássia Faria de Assis / Daniel Neves Gonçalves Schmitz / Marcelino A.Vieira da Silva

Metaheurística para o problema de roteamento de navios aliviadores...........................Pedro da Matta e Andrade Basilio / Bruno Salezze Vieira / Marcus V. Oliveira Camara / Glaydston Mattos Ribeiro

Optimización de localización de parques industriales....................................................Luis Enrique Vázquez Montes / Esther Segura Pérez

Índice en transporte urbano de carga..............................................................................Eduardo Betanzo-Quezada / José A. Romero Navarrete / Saúl A. Obregón Biosca / Eber González / Miguel A. Toral Luna

Localização de um hospital para epidemias de dengue..................................................Márcia M. Altimari Samed / Maycon A. dos Santos

Movilización de productos y subproductos de la Faja Petrolífera del Orinoco.............Patricia López

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Accidentalidad y logística del transporte de materiales peligrosos................................María G. Saucedo Rojas / Ana C. Cuevas Colunga / Jaime G. Pérez Castro / Alberto Mendoza Díaz

Intelligent packaging in urban logistics..........................................................................Ana P. Reis Noletto / Sérgio Adriano Loureiro / Rodrigo Barros Castro / Orlando Fontes Lima Jr.

Distribución urbana de mercancías: tendencias y políticas públicas..............................Juan Pablo Antún / Rodrigo Alarcón

Propuesta para distribución en Coyoacán.......................................................................Luis Reynaldo Mota Santiago / Angélica Lozano

Dinámica de sistemas para analizar niveles de servicio.................................................Conrado A. Serna Urán / Martín D. Arango Serna / Miguel A. Ortiz

Respuesta ante la ruptura en la cadena de suministro....................................................Ricardo Aceves García / Carmen I. Rodríguez Varona / Zaida E. Alarcón Bernal

Empacotamento de Ajuda Humanitária na Última Milha..............................................Juliano Souza / Leonardo Varella / Mirian Buss Gonçalves

Optimización reactiva de itinerarios de aviones cargueros............................................Julio Mora Olivares / Felipe Delgado Breinbauer

Governance in platforms through ICT...........................................................................Leonardo Varella / Mirian Buss Gonçalves / Regina Meyer Branski / Orlando Fontes Lima Junior

Load zone infrastructure in southern Europe..................................................................Jesús Muñuzuri / André Alho / João Abreu e Silva

Optimización de distribución de Gasolina......................................................................Esther Segura Pérez / Ann Godelieve Wellens / Alan A. Gómez Hernández / Nydia L. Rojas Mejía / Daniel A. Tello Gaete

Diseño de rutas de recolección de residuos sólidos en CU...........................................Carlos Adrián Enríquez Santillán / Angélica Lozano

Impacto socioeconómico del ferrocarril de mercancías extremeño...............................Juan Francisco Coloma Miró / Marta García García

Análise de eficiência dos terminais que operam na cabotagem.....................................Tafarel de Carvalho Gois / Reinaldo Moreira Del Fiaco / José Soares Pires / Alessandro Aveni / Paulo R.Vieira de Almeida

Modelos de redes y equilibrio oferta-demanda de transporte

Strategies for reducing transportation services...............................................................Francisco A. Ortega Riejos / Juan A. Mesa López-Colmenar / Miguel A. Pozo Montaño / Justo Puerto Albandoz

Surrogate-based optimization for tolling........................................................................Daniel Rodríguez Román / Stephen G. Ritchie

Flow-Queue-Time Dependent Traffic Modeling for Urban Networks...........................Gloria Londoño / Angélica Lozano

Origen-destino de viajes en sistema de transporte UNAM............................................Sonia Marcela Cifuentes Martínez / Angélica Lozano

Demanda por transporte terrestre desde aeropuertos......................................................Alejandra Lizana / Felipe Delgado / Ricardo Hurtubia / David Palma

Exact Model for LTL Location-Routing Problem..........................................................André Alarcon de Almeida Prado / Nicolau Dionísio Fares Gualda

Multicriteria framework for reliable aid distribution.....................................................Fabiola Regis / Jaime Mora-Vargas / Angel Ruiz

Linhas alimentadoras para o BRT sul de Brasília-DF....................................................Roberto Bernardo da Silva / Evaldo C. Cavalcante / José Matsuo Shimoishi / Tiago Luiz Messias / Alessandro Silva Barbosa

Simulación tiempos de espera sistema Bicipuma..........................................................Ricardo Torres Mendoza / Esther Segura Pérez

Políticas de transporte sostenible

Trolebuses y Electromovilidad Ciudad de México.........................................................Francisco G. Alvarado Arias

Movilidad en las zonas urbanas periféricas de difícil acceso.........................................Daniel Pérez-Rodríguez / Ana L. Flechas Camacho / Fredy L. Espejo Fandiño

Mobilidade, um termo a dissecar....................................................................................Henrique Eduardo Araújo Coelho / Rogério Faria D’Avila

Bicicletas compartilhadas em um campus universitário.................................................Caio Moura Vieira / Pastor Willy Gonzales Taco / Zuleide Oliveira Feitosa

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Evolution of transport policies in Latin-America...........................................................Carlos Alberto Moncada A. / Peter Jones / Juan Pablo Bocarejo S.

Ciclofaixa em área edificada: Salvador – Brasil.............................................................Anderson de Almeida Matos / Denise M. da Silva Ribeiro / Ilce M. Dantas Pinto / José L. de Carvalho / Juan P. Delgado

Impacto BiciMAD hábitos movilidad ciclista................................................................Andres Garcia-Martinez / Andres Monzon / Andras Muncaksy / Roberto Lillo

Sustainable performance assessment of urban-passenger transport...............................Vanessa de Almeida Guimarães / Ilton Curty Leal Junior / Pauli Adriano de Almada Garcia

A metaheuristic approach for repositioning problems in bike sharing...........................Javier Garcia-Gutierrez / Javier Romero-Torres / Manuel González de la Rosa

Walking to elementary schools.......................................................................................Suely da Penha Sanches / Marcos Antonio Garcia Ferreira

Identification of potential cyclists in a university campus.............................................Marcos Antonio Garcia Ferreira / Suely da Penha Sanches

Táxis vs. Uber: conflitos regulatórios no Brasil.............................................................Laize Andréa de Souza Silva / Maurício Oliveira de Andrade

Modelación de la elección de la bicicleta en ciudades...................................................Oscar Arbeláez Arenas / Iván Sarmiento Ordosgoitia / Jorge Córdoba Maquilón

Estimating bicycle demand in an aggressive environment.............................................Margareth Gutiérrez Torres / Victor Cantillo Maza / Julián Arellana Ochoa / Juan de Dios Ortúzar Salas

Metodología en modelos de elección la variable latente seguridad...............................Laura Inés Agudelo Vélez / Jorge Eliecer Córdoba Maquilón / Iván R. Sarmiento Ordosgoitia / Ángela B. Mejía Gutiérrez

City-HUBs: Urban Transport Interchanges....................................................................Andrés Monzón / Sara Hernández / Ana Barberán

Seguridad en sistemas de transporte

Seguridad Vial - HSM-2010............................................................................................Stefany Ramírez Hurtado / Yury Nathalia Ruiz Tiria

Análise de roubos de carga no sul no Brasil...................................................................Mário José Pinheiro da Rocha / Letícia Dexheimer / Fernanda David Weber

Safety of roundabouts using traffic conflicts..................................................................Lenin Alexander Bulla Cruz / Liliana Lucía Lyons Barrera

Accident Analysis of BRT in Mexico.............................................................................Vladimir Ávalos-Bravo / Jaime Santos-Reyes

Modeling of the perception of risk of accidents in drivers.............................................Thomas Edison Guerrero Barbosa / Víctor Alejandro Pachón Pineda / Jesús Alberto Rivera Zabaleta

Experiences and lessons learned from the sol project initiative implementation..........Miroslava Mikusova

Plataforma geográfica de la red carretera.......................................................................Ana Cecilia Cuevas Colunga / Jaime Guillermo Pérez Castro / Gerardo Ríos Quezada

Carretera 2+1. Solución para México.............................................................................Emmanuel Muñoz García / Ana Cecilia Cuevas Colunga

Modelo de red vial georreferenciado..............................................................................Noelia Villegas Villegas / Alberto Mendoza Díaz

Enfoque de Sistema Vial Seguro en México..................................................................Alberto Mendoza Díaz / Nadia Gómez González

Siniestralidad del usuario vulnerable en carreteras........................................................Emilio Fco. Mayoral Grajeda / Cecilia Cuevas Colunga

Variáveis explicativas dos acidentes de trânsito.............................................................Mauricio Renato Pina Moreira / Anísio Brasileiro de Freitas Dourado

Frecuencia de accidentes carreteros y factores determinantes.......................................Andrea S. Arévalo / Mauricio J. Orozco / Victor M. Cantillo

Comparación estadística: modelo iRAP y siniestralidad...............................................Guillermo Pérez Castro / Cecilia Cuevas Colunga / Guadalupe Saucedo Rojas / Alberto Mendoza Díaz

Simulador para evaluar seguridad en autopistas en Puerto Rico...................................Didier Valdés Díaz / Benjamín Colucci Ríos / Johnathan Ruiz Gonzalez / Bryan Ruiz Cruz / Ricardo García / Enid Colón

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Sistemas inteligentes de transporte y tecnologías de información

E-aprovisionamiento en el comercio exterior cubano.....................................................Jorge Moya Rangel / Martha Inés Gómez Acosta

ATIS for the Public Transport System of Ciudad Universitaria, UNAM........................David López / Angélica Lozano

Real Time Traffic Models Vienna Torino.........................................................................Luca Paone / José Vicente Torres Garibay

La concentración y habilidad para conducir....................................................................Fátima Pereira da Silva

Avaliação de ferramentas assistivas ao transporte...........................................................André Marques Cavalcanti Filho / André arques Cavalcanti

Análise das (TIC) do BRT Sul de Brasilia-DF.................................................................Roberto Bernardo da Silva / Evaldo Cesar Cavalcante Rodrigues / José MatsuoShimoishi / Adelaida Pallavicini Fonseca

Planning for the implementation of an Adaptive Traffic Control System.......................Angélica Lozano / Francisco Granados / Alejandro Guzmán

Transporte y medio ambiente

A road and environmental pricing methodology.............................................................Ricardo Montoya Zamora / José A. Romero Navarrete / Eduardo Betanzo Quezada / Saúl A. Obregón Biosca

Impacto social de de la transición entre planes de semaforización.................................Rita Peñabaena-Niebles / Victor Cantillo / José Luis Moura

Alternativas de solución para un sistema de RSU...........................................................Zaida Estefanía Alarcón Bernal / Ricardo Aceves García / Omar Rivas Martínez

Mezclas asfálticas tibias: medioambientalmente más amigables....................................Jorge Eliécer Córdoba Maquilón / Vanessa Senior Arrieta / Deisy Johana Posada

Plan Maestro de Movilidad de San Andrés......................................................................Lizbeth Johanna López Camacho / Luis Ernesto Sánchez Amaya / Diana Patricia Ardila Luengas

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O-D Matrix adjustment by conjugate gradient..............................................................María Victoria Chávez Hernández / Lorenzo Héctor Juárez Valencia

Análise da utilização do Bilhete Único do Rio de Janeiro em megaeventos................Thayse Ferrari / Carlos David Nassi / Igor Andrade Rocha / Gabriel Tenenbaum de Oliveira

Rapid Rail Transit Integrated Recovery.........................................................................Luis Cadarso / Ángel Marín

A planning tool for public transport analysis................................................................. Sebastián Raveau / Juan Carlos Muñoz / Carlo G. Prato

Modelling passenger distribution and interaction..........................................................Sebastian Seriani / Taku Fujiyama / Catherine Holloway

Diretrizes para investimentos em transporte - urbanístico.............................................Maria Ivana Vanderlei / Leonardo Herszon Meira / Oswaldo Cavalcanti da Costa Lima Neto / Maria Leonor Alves Maia

Transporte y uso del suelo.

Paradigma de planificación del estacionamiento vehicular...........................................Fredy Leandro Espejo Fandiño / Daniel Alejandro Pérez Rodríguez

Accesibilidad mediante transporte público....................................................................Ignacio Tiznado-Aitken / Juan Carlos Muñoz / Ricardo Hurtubia

Geração de renda urbana, mobilidade............................................................................Clóvis Garcez Magalhães / Luiz Afonso dos Santos Senna

Impacto de la GMVV en el sistema de transporte.........................................................Adarenis García Alarcón

Teoría de autómatas celulares y cambio de uso del suelo.............................................Gustavo Camacho Palacios

Work-accessibility and mobility equity in Bogotá........................................................Luis A. Guzman / Carlos Rivera / Daniel Oviedo

Build of environment characteristics to promote walkable neighborhoods..................Ana Margarita Larranaga / Helena B. Bettella Cybis / Julián Arellana / Luis Ignacio Rizzi / Orlando Strambi

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PREFACIO La Sociedad Panamericana de Investigaciones en Transporte (PANAMSTR, por sus siglas en inglés) promueve la investigación en transporte y sistemas sustentables de transporte y logística a través de un foro para el intercambio de ideas en las Américas, España y Portugal. Cada dos años organiza el Congreso Panamericano de Ingeniería de Tránsito, Transporte y Logística, PANAM, que es la conferencia de transporte más importante de Ibero-América y se ha convertido en un lugar de encuentro no sólo para académicos y profesionales, sino también para ejecutivos de empresas y funcionarios públicos de América, España y Portugal y varios otros países del mundo. Es una oportunidad para presentar y discutir acerca de los avances de la investigación, el desarrollo metodológico, técnico y tecnológico en sus temas pilares: tránsito, transporte y logística. El PANAM ha sido realizado en varias ciudades desde 1980, cuando fue su primera edición. En su más reciente versión, el XIX Congreso Panamericano de Ingeniería de Tránsito, Transporte y Logística (PANAM2016) fue realizado en la Ciudad de México, entre el 28 y el 30 de septiembre de 2016, organizado por el Grupo de Investigación en Ingeniería de Transporte y Logística (GiiTraL) del Instituto de Ingeniería de la Universidad Nacional Autónoma de México (UNAM). El presente documento engloba una pre-edición de los artículos que luego de ser arbitrados fueron aceptados. Estos artículos presentan el análisis de las problemáticas de ingeniería de tráfico, transporte y logística en esta parte del mundo, las cuales son comunes en muchos de nuestros países. Agradecemos a los autores de los artículos sometidos al PANAM2016, por sus aportaciones, y a los miembros del comité organizador por su apoyo para llevar a cabo este evento. Angélica Lozano Presidenta del Comité Organizador del PANAM 2016

1338 1339Transporte público XIX Congreso PANAM

O-D Matrix adjustment by conjugate gradient O-D Matrix adjustment by conjugate gradient

Demand adjustment for the transit network of Mexico City and its surroundings

María Victoria Chávez Hernández Lorenzo Héctor Juárez Valencia

Universidad Autónoma Metropolitana - Iztapalapa, México

ABSTRACT Estimating or adjusting an origin-destination demand matrix from previously known data is an important, some times critical, issue for public transportation systems. In this paper we employ a multiplicative conjugate gradient algorithm to estimate the origin destination matrix, based on observed volumes on a given set of segments. We show that this algorithm improves the performance of the traditional multiplicative steepest descent algorithm, introduced by Spiess in 1990. The proposed algorithm is programmed in the macro language of EMME/4 and is tested in a synthetic scenario for the transit network based on Mexico City (1705 zones). Keywords: O-D matrix, bi-level programming, transit network, conjugate gradient. 1. INTRODUCTION During the last five decades researchers have made a significant progress on the development of methods for recovering an origin-destination matrix (O-D matrix) from observed data in transportation networks. Most of those methods are designed for the study of traffic networks and only a relative small number of them are developed for public transportation systems. In the literature such methods are classified into two big groups (Bera and Rao, 2011): static and dynamic. For static methods the volumes (of vehicles or travelers) do not depend of time and the models are thought for long-term planning. For dynamic models the volumes are time-dependent and the methods are designed to control the flow of vehicles over the network or to suggest routes to travelers. In general, computing an O-D matrix from observed link volumes gives rise to a problem with more unknown variables than independent constraints, and the solution is not unique. Then, some models look for the closest O-D matrix to a given obsolete one, under some assumptions, such as the structure of the matrix or trip information for some O-D zones. See,

for instance, references Van Zuylen and Willumsen (1980), Spiess (1987), Spiess (1990), Bierlaire (1995), Codina et al. (2006), Lundgren and Peterson (2008), Noriega and Florian (2009). The most popular approaches formulate the problem as a convex optimization one, where the objective function corresponds to a regression model. Constraints are used to force the matching between the assigned volumes and the observed ones. These problems can be reformulated as least squares models where the volume constraints are relaxed and incorporated into additional terms in the objective function. Least squares models have been studied and extended over the years (Cascetta, 1984; Cascetta and Nguyen, 1988; Bierlaire, 1995; Noriega and Florian, 2009), they are mainly inspired on a maximum likelihood estimation method, considering that the obsolete matrix follows a multivariate normal distribution, and they are part of the well known bi level programs (Codina et al., 2006; Codina and Barceló, 2000; Lundgren and Peterson, 2008). An important issue on these programs is finding a good algorithm to solve efficiently the corresponding problem for large-scale networks, where the computational cost to estimate an O-D matrix increases considerably. During the last decades, gradient-based methods have been proposed (Spiess, 1990; Bierlaire, 1995; Florian and Chen, 1995; Codina and Barceló, 2000; Codina, 2002; Codina et al., 2006; Lundgren and Peterson, 2008). For instance, consider the resulting demand matrix pqg g

where pq PQ denote O-D pairs; Spiess (1990) proposed a multiplicative steepest descent (MSD) method to estimate this O-D matrix with the solution of the following problem:

21 ˆmin ( )2 a ag a A

Z g v g v

(1)

s. t. ( )v g assign g and 0,pqg pq PQ (2)

where A A is the subset of links where counts are available and A the set of all links on the network, ˆ ˆa a A

v v

and ( ) ( ) ( )a a Av g assign g v g

represent the observed volumes

and the volumes obtained after an assignment process with the matrix g, respectively. This assignment process must correspond to a convex optimization problem and it is understood as an equilibrium assignment to ensure the convexity of the model, see Florian (1977). In that work congestion effects were not considered. Problem (1)-(2) has an infinite number of solutions, and a criterion is needed to select only one of them. Spiess proposed to choose the closest solution to a given obsolete matrix g . He introduced the following multiplicative steepest descent method:



1

ˆ for 0,

( )1 for 1,2,..., .

pq

l lpq l l

pqpq

g l

g Z gg l Lg

(3)

This multiplicative algorithm keeps the structure of the prior (obsolete) matrix, and its simplicity makes it applicable to large-scale networks. This algorithm is part of the EMME/4 transportation planning system (INRO, 2015). In a previous work we solved the equilibrium transit assignment problem on an available transit network of Mexico City and its surroundings, employing the software system EMME/4 (see Juárez et al., 2013). This model, introduced by Spiess and Florian (1989), is based on the concept of optimal strategies and it allowed us to reproduce some scenarios of the real system: we obtained the impact of the total demand on the subway system and the total times during the peak hours in the morning of a normal day. Although our results replicate some features of this public transportation system, it is important to notice that the transit network is obsolete, since the most recent information in the database was included in 2010. In recent years a new subway line was added, as well as many other lines for other modes of transportation; also the public transportation system has been reorganized. Furthermore, the O-D matrix was built up in 2007 and its last update occurred in 2012. This situation motivated us to consider the problem of estimate an O-D matrix from an obsolete one. In 2014, we adapted the ideas of Spiess (1990) and Noriega and Florian (2009) to estimate an O-D matrix for a transit network (Chávez and Juárez, 2014). Additionally, we proposed a penalized model based on generalized least squares and we solved it by a multiplicative conjugate gradient (MCG) algorithm applied to the transit network of Winnipeg. Subsequently, in 2015, we tested our model with different values for the penalty parameter and compared the results obtained with the methodology of Spiess (Juárez and Chávez, 2015). Those numerical results showed that the computational cost of Spiess’s methodology is higher than the computational cost of our methodology. In this paper we show that the methodology used before can be successfully applied to much bigger transit networks, like the network of Mexico City and surroundings. The paper is organized as follow: in section 2 the O-D matrix estimation problem is described, in section 3 we describe the multiplicative conjugate gradient algorithm used in this paper, in section 4 we show some results for the transit network of Mexico City and finally, in section 5 we give some conclusions.

2. THE O–D MATRIX ADJUSTMENT PROBLEM Given an obsolete O-D matrix, denoted by ˆ ˆ pqg g , we aim to find a new O-D matrix

pqg g , close to g , such that the resulting volumes (after a linear assignment of g) are

equal or very near to the observed volumes ˆ ˆ ,av v a A . More precisely, we want to

find an O-D matrix g that solves:

21 ˆmin ( )2 pq pqg pq PQ

Z g g g

(4)

s. t. ˆ ( ),a av v g a A (5)

( ) ( )av g assign g . (6) Problem (4)–(6) is a variant of a control (or inverse) problem and it is ill–posed. So, to find a solution, a regularization procedure is needed first. Actually, problem (4)–(6) can be thought as one in which we want to take the transit system to a desired state given by (5), using a control variable: the demand matrix g. To find a solution, equation (5) is relaxed and we look for a demand matrix g such that ( )av g is as close as possible to ˆav for each a A . This is achieved penalizing the differences between these two quantities and adding them to the objective function. We obtain the following problem

2 21 1ˆ ˆmin ( ) ( ) ,2 2pq pq a a ag pq PQ a A

Z g g g k v g v

0ak (7)

s. t. ˆ( ) ( )a av g assigng g v and 0pqg pq PQ , (8)

where ak is a penalty parameter for each a A . Thus, condition (5) is enforced very

accurately with high values of ak , and this is demonstrated by the numerical results. It is possible that the measured volumes are more reliable or accurate on some segments than on others, and we may choose different values of ak for each segment. Of course, a simple

scheme is to choose ak = k >0 for all a A . For instance, problem (7)-(8) is equivalent to the

model proposed by Noriega and Florian (2009) when / (1 )ak

22 1ˆ ˆmin ( ) ( ) ,2 2a a pq pqg a A pq PQ

Z g v g v g g

0 1 . (9)



For us, it is more intuitive to use the penalty parameter ak , because it indicates directly the given weight to the difference of volumes. In this paper we shall use a constant penalty parameter k. 3. A MULTIPLICATIVE CONJUGATE GRADIENT ALGORITHM In the simplest case, the conjugate gradient algorithm to solve problem (7)-(8) can be formulated as follows:

1ˆ for 0,

for 1,2,..., .pqll lpqpq l pq

g lg

g d l L

.pq PQ (10)

In (10), l l

pqd d is a conjugate direction vector at iteration l and l is the length step that

minimizes the objective function along that direction. The starting value of the iterative process in (10) is the obsolete O-D matrix g . In a planning context, the resulting matrix is expected to resemble as closely as possible the initial matrix, since it contains important structural information on the O-D movements. Following this idea, Spiess proposed the multiplicative iteration formula given by (3), which has the following properties: 1) a change in demand is proportional to the demand of the initial matrix, and 2) null coefficients are preserved (Spiess, 1990). Applying this idea to the conjugate gradient method, the iterative algorithm can be reformulated in the following way

1

ˆ for 0,

1 for 1,2,..., ,pql

pq l lpq l pq

g lg

g d l L

pq PQ . (11)

The new conjugate direction 1l

pqd is generated with a linear combination of the previous

conjugate direction and the current gradient. Thus

1( ) , ,l

l l lpq pq l pq

pq

Z gd g d pq PQg

(12)

and the constant l is such that the two directions l

pqd and 1lpqd

are conjugate to each other.

Notice that in (12) we have multiplied the gradient by lpqg to preserve the multiplicative

structure of the algorithm. The gradient in (12) can be computed from (7) using the chain rule

11

1 1 ( )( ) ˆ ˆ( ) , ,ll

l l apq pq a a

a Apq pq

v gZ g g g k v g v pq PQg g

(13)

where we still need to compute the derivative of the flows ( )av g . These segment volumes can be expressed as:

1 0 if ,( ) , , and :

1 if ,pq

la as s as

pq PQ s S

a sv g h a A

a s

(14)

pqS represents the set of used paths in the network to go from p to q, and sh denotes the total

flow along one path pqs S . Equation (14) can be rewritten in terms of the path probabilities 1 1/l l

s s pqh g , pqs S , pq PQ :

1 1 1( ) , .

pq

l l la pq as s

pq PQ s Sv g g a A

(15)

Assuming that 1l l

s s , we get

1( ) , , .pq

lla

as ss Spq

v g a A pq PQg

(16)

Therefore, from (13) and (16) we obtain

1

1 1( ) ˆ ˆ( ) , .pq

ll l lpq pq s as a a

s S a Apq

Z g g g k v g v pq PQg

(17)

Note that the assumption 1l l

s s is very reasonable, especially when the sequence {gl} is

close to the optimum. It simplifies the computation of the gradient ( )Z g and also gives a

“linear behavior” to ( )av g , since ( ) ( ) ( )a a av g d v g v d for d small.

The optimal step length l in (11) is the minimum of the one-dimensional quadratic function

l ll lZ g d . More precisely, it solves the problem



2 21 ˆ ˆmin ( ) ( ) , 0,2 2

l l l ll pq l pq pq a l a a

pq PQ a A

kg d g v g v d v k

(18)

s. t. 1lld , and 0l

pqg , pq PQ , (19)

which solution is

2 2

ˆ ˆ( ) ( )

( )

l l l lpq pq pq a a a

pq PQ a Al l l

pq apq PQ a A

d g g k v d v v g

d k v d

. (20)

After obtaining gl+1, the new conjugate direction is computed using formula (12), where the value of l is calculated with an adapted variant of the Hestenes-Stiefel formula (Nocedal and Wright, 2006):

1 11

1

( ) ( ) ( )

( ) ( )

l l llpq

pq PQ pq pq pql l l

lpq

pq PQ pq pq

Z g Z g Z ggg g g

Z g Z gdg g

(21)

Notice that we have multiplied each term in the numerator by 1l

pqg

in order to keep the

multiplicative structure of the iterative algorithm. Therefore, the multiplicative conjugate algorithm is: Algorithm 1: Multiplicative conjugate gradient for O-D matrix adjustment.

Initialization. Given the initial obsolete demand 0 ˆg g and the observed volumes ˆav , do the following: 1. Solve the problem 0 0( ) ( )v g assign g to get the segment flows and compute the

gradient0( )

pq

Z gg

with equation (17).

2. Compute the initial direction: 0

0 ( )pq

pq

Z gdg

, pq PQ .

Descent. For 0l , assuming we know lg , ld , do the following steps:

3. Solve the problem ( ) ( )l lv d assign d .

4. Compute l using formula (20) with the known values lg , ld , ( )lv g , ( )lv d .

5. Update the demand matrix: 1 1l l lpq pq l pqg g d , pq PQ .

6. Compute the gradient of the objective function at 1lg : apply formula (17). Stopping criterion and new descent direction. Given 0 1 (the stopping parameter), do the following: 7. If 1 0( ) ( )lZ g Z g , take 1lg g , stop and exit.

8. Otherwise, compute l with formula (21).

9. Compute the new conjugate gradient direction 1ld with formula (12). 10. Update the index: l=l+1 and return to step 3. 4 NUMERICAL RESULTS The following numerical calculations were done in a HP computer with an Intel(R) Xenon(R) 3.4 GHz processor and 16 GB RAM by using EMME/4 software with a license size 12 (INRO, 2015). We consider the transit network of Mexico City, which consists in 1705 centroids, 7241 regular nodes, and 31720 links, 18 modes of public transportation, which are divided into transit, traffic and auxiliary modes. Traffic modes include private cars; transit modes include: subway, subway rail, light rail, tram, trolleybus, mexi-bus, among others; auxiliary modes are: subway correspondences, conveyors, access to metro-bus, suburban and pedestrian accesses. The network contains 845 transit lines that lead to 47004 segments. Engineers, from the sub-direction of strategic planning at METRO (i.e. the subway system), were able to calibrate all the parameters needed for the simulations, including the mean time of boarding, capacity of the public vehicles, volume-delay functions, capacity of the different vehicles for the different lines, headways, among many other values. The network is displayed in Figure 1, where the set of segments with available counts ( A ) are shown in red. The O-D matrix g used for these results is an updated projection of the demand matrix obtained by an O-D survey applied in Mexico City and neighboring municipalities in 2007, and subsequently updated in 2012. This matrix estimates the mobility on Mexico City during the morning from 6:00 to 9:00 am. In order to calibrate the proposed methodology, we constructed the following scenario: we did a transit assignment on this network with a previously known O-D matrix g at the peak hour in the morning; from this result we extracted the volumes, which play the role of measured volumes in the numerical experiments. Next, we generated an O-D matrix g , disturbing stochastically the O-D matrix g by 20%. Then, with these data, we applied the multiplicative steepest descent (MSD) and the multiplicative conjugate gradient (MCG) algorithms, employing different values of the penalty parameter k. The MSD algorithm is depicted in (3) and the MCG algorithm is our proposal introduced



above. To stop the iterations of the MCG (step 7) and of the MSD algorithms we choose 310 . Our main interest is to test the ability of these algorithms to recover the original

demand matrix g and the volumes ˆav , a A , as well as the number of iterations and CPU time.

Fig. 1- Segment counts on the transit network of Mexico City. Table 1 shows the values of a least squares fit of the deviation from the original O-D matrix obtained with both iterative algorithms, MSD and MCG. Similarly, table 2 shows the correspondent values of the least squares fit of the adjusted volumes versus the real volumes. In both tables, the parameters b and m denote the parameters of the regression line, thus the

adjustment is better for those points that are closer to the correspondent line. The values 2Rand RMSE denote the correlation coefficient and the square root of the mean squared error, respectively. More detailed information about the specific formulas to compute the regression parameters can be found in Chávez (2014) and Draper and Smith (1998). We also show the number of iterations to achieve convergence, to the given accuracy, as well as the required computational time (CPU) in seconds. Finally, in the last column we included the

values of the sums 2ˆpq pq

pq PQg g

and 2ˆ( )a aa A

v g v

, respectively.

k Method b m 2R RMSE Iters. CPU (s) 2ˆpq pq

pq PQg g

100 MSD 0.526 0.944 0.991 31.252 187 5920 19106.20 MCG 0.531 0.944 0.991 31.278 50 1617 19083.55

1000 MSD 0.509 0.944 0.991 31.253 190 5905 19140.27 MCG 0.457 0.945 0.991 31.225 75 2431 19401.58

10000 MSD 0.508 0.944 0.991 31.254 190 6014 19142.47 MCG 0.471 0.945 0.991 31.243 52 1692 19342.32

MSD 0.504 0.944 0.991 31.252 192 6016 19159.23 MCG 0.504 0.944 0.991 31.252 47 1548 19361.01

Table 1 - Demand deviation regression coefficients and convergence of MSD and MCG.

k Method b m 2R RMSE Iters. CPU (s) 2ˆ( )a aa A

v g v

100 MSD -11.934 1.000 1.000 66.902 187 5920 6715.08 MCG -11.546 1.000 1.000 68.603 50 1617 7053.87

1000 MSD -10.747 1.000 1.000 66.481 190 5905 6620.50 MCG -8.124 1.000 1.000 60.207 75 2431 5401.62

10000

MSD -10.739 1.000 1.000 66.479 190 6014 6620.04 MCG -8.982 1.000 1.000 62.109 52 1692 5747.93

MSD -10.538 1.000 1.000 66.058 192 6016 6533.78 MCG -10.538 1.000 1.000 66.058 47 1548 5877.18

Table 2 - Volume deviation regression coefficients. Numerical results in Table 1 show that the MSD algorithm does much more iterations than the MCG algorithm to achieve the same accuracy: for k = 1000 and (limiting cases), it does 3.6 and 4 times more iterations than the MCG, respectively. The CPU time employed with both algorithms exhibits the same ratio, i.e. the MCG algorithm is about four times faster than the MSD algorithm to compute the same O-Matrix. Thus, the additional work to compute l in (21) at each iteration of the MCG algorithm is marginal with respect to the overall calculation.



Concerning to the influence of the penalty parameter, it can be observed that for the MCG algorithm the numerical results remain almost the same. Figures 2 and 3 are plots of the demand deviations and flow comparison for k =1000, and Figures 4 and 5 for k=∞, respectively. These two figures also corroborate that the results obtained with the MSD algorithm are quite similar to those obtained with the MCG algorithm.

Fig. 2 - Demand deviations for the MSD (left) and MCG (right) algorithms with k = 1000.

Fig. 3 - Flow deviations for the MSD (left) and MCG (right) algorithms with k = 1000.

Fig. 4 - Demand deviations for the MSD (left) and MCG (right), obtained with the model of Spiess.

Fig. 5 - Demand deviations for the MSD (left) and MCG (right), obtained with the model of Spiess. Finally, Figure 6 shows the decrease of the objective function for the first 45 iterations whenk .

Fig. 6 - Objective function vs. iteration for MSD and MGC algorithms for the model of Spiess.



5 CONCLUSIONS We studied an O-D matrix demand adjustment model for transit networks, which is based on available volume data on some known segments. This model was introduced in a previous work (Chávez and Juárez, 2014), and it is a variant of known existing models. It incorporates the constraints as penalized terms to the objective function; see (7)–(8). To solve the optimization problem we employed a multiplicative conjugate gradient algorithm. The performance of this algorithm was compared with the method of steepest descent of Spiess (1990). Both methods produced very similar solutions, but with the advantage that the conjugate gradient algorithm does much less iterations to get the same accuracy and, consequently, it is about 3.5 to 4 times faster than the steepest descent algorithm of Spiess, at least for the transit network considered in this work. Initially, we thought that a potential drawback of the MCG algorithm could be that it does more flops per iteration than the MSD algorithm, mainly due to the computation of l with (21). However, this is not the case, since the ratio of CPU between both algorithms is about the same than the ratio of number of iterations, which suggest that the additional CPU time to compute l is marginal. There are additional issues that we still need to investigate further, like the convergence properties of the MCG algorithm, which is related to the behavior of the conjugate directions

ld in the iterative process. Also, it will be interesting to apply the general penalized model (7)–(8), allowing different penalization parameters for different segments. Also, it may be possible to improve the performance of the MCG algorithm with a good preconditioner in order to reduce further the number of iterations. A pending task is to test how our approach compares with more recent models and techniques, like bi level programming techniques, but in the context of transit assignment. Finally, we want to comment that an important case arises with scenarios where congestion plays a strong role. In this case transit assignment with a linear basic model may not be a valid choice to update the O-D matrix, because the optimization program is not longer convex. This is a crucial issue for large networks in big metropolitan areas, which are commonly congested at peak hours. This drawback is also shared by the steepest decent method of Spiess. Large transit networks may require a different approach, for instance a heuristic algorithm to get closer to a minimum, and then switch to a traditional descent algorithm when approaching to the optimal value.

ACKNOWLEDGEMENTS We acknowledge the help of the sub-direction of strategic planning at METRO (subway system in Mexico City) and the engineers who facilitated us all the information and databases they collected and constructed over the years; and also for sharing their projects and problems. We also want to thank Professor Michael Florian and his assistant, Yolanda Noriega, for their hospitality, help and advice to the first author, when she was doing an internship at CIRRELT (University of Montreal) to get training in the use of EMME/4 software. Also, we would like to acknowledge the financial support of the math graduate program at UAM-Iztapalapa and the Mathematics and Development Network of CONACYT in México. REFERENCES: BERA S. AND RAO K. (2011). Estimation of Origin-Destination Matrix from Traffic Counts: the State of the Art. European Transport (49), pp. 3-23. BIERLAIRE M. (1995). Mathematical Models for Transportation Demand Analysis. Ph.d. thesis, Facultés Universitaires Notre-Dame de la Paix de Namur, Faculté des Sciences, Départment de Mathématique, Namur. CASCETTA E. (1984). Estimation of trip matrices from traffic counts and survey data: a generalized least squares estimator. Transportation Research Part B: Methodological 18, pp. 289-299. CASCETTA E. AND NGUYEN S. (1988). A Unified Framework for Estimating or Updating Origin/Destination Matrices from Traffic Counts. Transportation Research Part B 22B(6), pp. 437-455. CHÁVEZ M. (2014). Modelos matemáticos para análisis de demanda en transporte. Master’s thesis, Universidad Autónoma Metropolitana-Iztapalapa, Department of Mathematics, Ciudad de México. CHÁVEZ M. AND JUÁREZ L. (2014). A Multiplicative Conjugate Gradient Method for the O-D Adjustment Matrix. R. Z. Ríos-Mercado et al. (Eds.): Recent Advances in Theory, Methods, and Practice of Operations Research, pp. 97-104. CODINA E. (2002) Consistency of an Approximation to the Upper Level Objective Function Gradients in the O-D Demand Adjustment Problem. Tech. rep., Departament d’Estadística i Investigació Operativa, Universitat Politécnica de Catalunya, Sapain, research Report DR/2002-01. CODINA E. AND BARCELÓ J. (2000) Adjustment of O-D Trip Matrices from Traffic Counts: an Algorithmic Approach Based on Conjugate Directions. Proceedings of the 8th

Euro Working Group on Transportation,pp. 427-432.

1353XIX Congreso PANAM

Análise da utilização do Bilhete Único do Rio de Janeiro em megaeventos

1352 Transporte público

O-D Matrix adjustment by conjugate gradient

CODINA E., GARCIA R. AND MARIN A. (2006) New Algorithmic Alternatives for the O-D Matrix Adjustment Problem on Traffic Networks. European Journal of Operation Research 175(3), pp. 1484-1500. DRAPER N. AND SMITH H. (1998) Applied Regression Analysis, 3rd ed. John Wiley and Sons. FLORIAN M. (1977) An Improved Linear Approximation Algorithm for the Network Equilibrium (packet switching) Problem. IEEE Proc. Decision and Control,pp. 812-828. FLORIAN M. AND CHEN Y. (1995) A Coordinate Descent Method for the Bi-Level O-D Matrix Adjustment Problem. International Transactions on Operations Research 2(2), pp. 165-179. INRO (2015) The evolution of transport planning. Available athttp://www.inrosoftware.com/en/products/emme/index.php JUÁREZ L., FERNÁNDEZ A., DELGADO J., CHÁVEZ M., OMAÑA E. (2013) Asignación de tránsito en la red metropolitana del Valle de México y su impacto en el stc-metro. Contactos. Revista de educación en ciencias e ingeniería (90), pp. 85-95. JUÁREZ L. AND CHÁVEZ M. (2015) O-D Matrix Adjustment for Transit Networks by Conjugate Gradient Iterations. Revista Investigación Operacional 36(2), pp. 85-95. LUNDGREN J. AND PETERSON A. (2008) A Heuristic for the Bilevel Origin-Destination Matrix Estimation Problem. Transportation Research Part B: Methodological 42(4), pp. 339-354. NOCEDAL J. AND WRIGHT S. (2006) Numerical Optimization, 2nd ed. Springer Series in Operations Research and Financial Engineering. NORIEGA Y. AND FLORIAN M. (2009) Some Enhancements of the Gradient Method for O-D Matrix Adjustment. Tech. Rep. 4, CIRRELT. SPIESS H. (1987) A Maximum-Likelihood Model for Estimating Origin-Destination Matrices. Transportation Research Part B: Methodological 21(5), pp. 395-412. SPIESS H. AND FLORIAN M. (1989) Optimal Strategies: A New Assignment Model for Transit Networks. Transportation Research Part B: Methodological 23(2), pp. 83-102. SPIESS H. (1990) A Gradient Approach for the O-D Matrix Adjustment Problem. EMME/2 Support Center, Switzerland, http://www.spiess.ch/emme2/demadj/demadj.html VAN ZUYLEN H. AND WILLUMSEN L. (1980) The Most Likely Trip Matrix Estimated from Traffic Counts. Transportation Research Part B: Methodological 14B, pp. 281-293.

Análise comparativa da utilização do Bilhete Único Intermunicipal na Região Metropolitana do Rio de Janeiro com

o advento dos megaeventos sob a ótica dos usuários1

Thayse Ferrari [email protected]

Carlos David Nassi Igor Andrade Rocha

Gabriel Tenenbaum de Oliveira Universidade Federal do Rio de Janeiro, Brasil

RESUMO Com o advento dos megaeventos que a cidade do Rio de Janeiro tem recebido, o plano de mobilidade urbana de sua região metropolitana ganhou amplo destaque mundial, principalmente no que tange ao Sistema de Bilhetagem Eletrônica implantado pelo Governo do Estado, o Bilhete Único Intermunicipal (BUI). Neste contexto está inserido o principal problema deste estudo, qual o impacto dos megaeventos na demanda do sistema de bilhetagem eletrônica da Região Metropolitana do Rio de Janeiro (RMRJ) quando comparado ao comportamento cotidiano da mesma. Assim, este trabalho tem como objetivo principal traçar o panorama da demanda do BUI em meses de realização de um megaevento, de forma a averiguar as similaridades e diferenças no comportamento da mesma confrontado ao mesmo período do ano onde não ocorra a realização de eventos deste porte. Para tanto foram feitas pesquisas bibliográficas e documentais, cujos dados foram tratados de forma qualitativa, além de consultas ao banco de dados do BUI, que teve os dados extraídos tratados quantitativamente. Como principal resultado deste trabalho, foi possível visualizar as variáveis que mais sofrem alteração quando comparados períodos habituais e de megaeventos, de forma a explicar o comportamento dos usuários de transporte público nessas ocasiões. A redução no número de integrações em períodos de grandes eventos, por exemplo, mostrou-se compatível com os menores deslocamentos realizados pelos espectadores, quando comparado ao padrão habitual de deslocamentos pendulares característicos da RMRJ. Palavras-chave: Megaeventos, Smartcard data, Automatização da cobrança de tarifa, Impactos na demanda

1 Esta é uma versão resumida do artigo apresentado no congresso. A versão completa está sendo submetido a um periódico. Para mais informações, entre em contato com os autores.

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