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E S T R A U S 4.3 217 A1 FORMULACIÓN DEL MODELO A1.1 INTRODUCCIÓN Este anexo describe en detalle la formulación matemática del modelo ESTRAUS. La primera parte de este anexo, sección A1.2, provee una base teórica del modelo, que incluye una nota técnica con la formulación matemática general del problema de equilibrio simultáneo, y la referencia a un trabajo publicado que presenta la modelación de transporte público considerada en ESTRAUS (conceptos de sección de ruta, restri
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    E S T R A U S 4.3 217 A1 FORMULACIÓN DEL MODELO A1.1 INTRODUCCIÓN Este anexo describe en detalle la formulación matemática del modelo ESTRAUS. La primera parte de este anexo, sección A1.2, provee una base teórica del modelo, que incluye una nota técnica con la formulación matemática general del problema de equilibrio simultáneo, y la referencia a un trabajo publicado que presenta la modelación de transporte público considerada en ESTRAUS (conceptos de sección de ruta, restricción de capacidad en transporte público, etc.). Estos artículos proveen información suficiente para familiarizar al usuario tanto con los conceptos utilizados en ESTRAUS, como con el modelo matemático asociado. La segunda parte de este anexo, sección A1.3, describe cómo el modelo general planteado en la nota técnica antes mencionada, está implementado en la actual versión de ESTRAUS, incluyendo las diferentes simplificaciones y el algoritmo de solución implementado. A1.2 BASE TEÓRICA El primer artículo incluido en esta sección, describe la formulación matemática general del modelo ESTRAUS, incluyendo los diferentes submodelos considerados (distribución de viajes, partición modal y asignación de tráfico),así como también la solución de equilibrio y las condiciones de optimalidad del problema. El segundo artículo, describe en detalle la red de servicios para la modelación del transporte público, la que es requerida para representar los efectos de congestión debida a la restricción de capacidad en estos servicios.  A1. FORMULACIÓN DEL MODELO 218   E S T R A U S 3.0   A1.2.1 ESTRAUS: A COMPUTER PACKAGE FOR SOLVING SUPPLY-DEMAND EQUILIBRIUM PROBLEMS ON MULTIMODAL URBAN TRANSPORTATION NETWORKS WITH MULTIPLE USER CLASSES  Joaquín de Cea Chicano, J. Enrique Fernández Larrañaga, Valérie Dekock Ch., Alexandra Soto O. y Terry L. Friesz.    ESTRAUS: A COMPUTER PACKAGE FOR SOLVING SUPPLY-DEMAND EQUILIBRIUM PROBLEMS ON MULTIMODAL URBAN TRANSPORTATION NETWORKS WITH MULTIPLE USER CLASSES Joaquín de Cea Ch., J. Enrique Fernández L., Valérie Dekock Ch. Departamento de Ingeniería de Transporte, Pontificia Universidad Católica de Chile Casilla 306, Santiago 22, CHILE FAX: (56-2) 686 4820; e-mail  jdc@ing.puc.cl  Alexandra Soto O. Fernández & De Cea Ingenieros Limitada Lota 2257, Providencia, Santiago, CHILE FAX: (56-2) 234 1575; e-mail asoto@FDCconsult.com and Terry L. Friesz Department of Systems Engineering and Operations Research, George Mason University Fairfax, VA 22030, USA e-mail tfriesz@gmu.edu  ABSTRACT Hmsghr o`odq vd oqdrdms ` lncdkhmf `ooqn`bg enq rnkuhmf pthsd fdmdq`krtookx,cdl`mc mdsvnqj dpthkhaqhtl oqnakdlr hmsqhmrhb sn sgd sq`mronqs`shnmok`mmhmf oqnbdrr- Sgd rnesv`qd hlokdldms`shnmne sgd lncdkcdrbqhadc gdqdhmhr jmnvm`r DRSQ@TR- Hs hr rhfmhehb`ms sg`s DRSQ@TR hr tmhptd `lnmf bnlldqbh`krnesv`qd enq sq`mronqs`shnmok`mmhmf adb`trd hs hlokdldmsr `kkne sgd jdx sgdnqdshb`k`mc `kfnqhsglhb `cu`mbdr hmrs`shb sq`eehb `rrhfmldms `mc ok`mmhmf sg`s g`ud `ood`qdc hmsgd khsdq`stqd ctqhmf sgd k`rs 1/ xd`qr- Hmo`qshbtk`q+DRSQ@TR hr `akd sn bnmrhcdq ` u`qhdsx ne cdl`mc lncdkr `mc sqho `rrhfmldms adg`uhnqr vhsghmsgd r`ld lncdkhlokdldms`shnmhmbktchmf ltkshokd trdq bk`rrdr `mc bnlahmdc sq`udklncdr sg`s hmsdq`bs nmsgd r`ld ogxrhb`kmdsvnqj- Sgd cdl`mc  bgnhbdr `qd rtoonrdc sn g`ud ` ghdq`qbghb`krsqtbstqd- Vgdmsgd sqho chrsqhatshnmhr u`qh`akd+` cntakx bnmrsq`hmdc dmsqnox,l`whlhyhmf lncdkhr bnmrhcdqdc `s sgd ehqrs kdudkne bgnhbd `mc ` ghdq`qbghb`kknfhs lncdkhr trdc enq sgd qdl`hmhmf cdl`mc bgnhbdr 'shld ne cdo`qstqd+lncd bgnhbd+sq`mredq onhms enq bnlahmdc lncdr+dsb-(- He sgd sqho chrsqhatshnmhr bnmrhcdqdc sn ad dwnfdmntr+sgd cdl`mc bgnhbdr `qd lncdkdc vhsg ` ghdq`qbghb`kknfhs- Nmd ne sgd lncdk     r l`hmed`stqdr hr sg`s hs bnmrhcdqr sgd deedbsr ne bnmfdrshnmnmsgd qn`c mdsvnqj `r vdkk`r hmd`bg otakhb sq`mronqs`shnmrdquhbd mdsvnqj- Cheedqdms oqnakdlr `qd l`sgdl`shb`kkx enqltk`sdc `r u`qh`shnm`khmdpt`khshdr+vhsg `rxlldsqhb bnrs etmbshnmr+`mc `kkne sgdl `qd rnkudc enkknvhmf sgd ch`fnm`khy`shnm`kfnqhsgl- D`bg hsdq`shnmne sgd `enqdldmshnmdc oqnbdctqd rnkudr `mnoshlhy`shnmoqnakdl trhmf Du`m    r `kfnqhsgl- Nmd ne sgd l`sgdl`shb`k enqltk`shnmr oqdrdmsdc hmsghr o`odq 'chrsqhatshnm,lnc`krokhs,`rrhfmldms( g`r addmhlokdldmsdc hmsgd k`sdrs udqrhnmne sgd bnlotsdq lncdkDRSQ@TR+vghbg hr o`qs ne ` a`ssdqx ne ok`mmhmf snnkr cdudknodc ax sgd fnudqmldms ne Bghkd sn rhltk`sd sgd nodq`shnmne `ksdqm`shud mdsvnqj bnmehftq`shnmr `mc du`kt`sd rsq`sdfhb cdudknoldms ok`mr enq tqa`msq`mronqs`shnmrxrsdlr- Hmsgd k`rs o`qs ne sgd o`odq+rnld `ookhb`shnmr ne DRSQ@TR cdudknodc hmBghkd ctqhmf sgd k`rs xd`qr `qd aqhdekx chrbtrrdc-    2 1. INTRODUCTION  An important number of big size metropolitan areas have experienced increasing levels of vehicular congestion, which in many cases has contributed to the serious pollution problems that affect these cities. Because of this, government authorities must often face demands from the  population and different interest groups in order to improve the operating conditions of the urban transportation systems and be pressured to build very expensive infrastructure projects (new metro lines, urban highways, etc.). Nevertheless, these options are very expensive for a developing country with very limited capital resources that have many alternative uses in different social areas such as education, health, housing and others. In the Chilean case, because of the need to make rational decisions with respect to the future development of their main urban transportation systems (beginning with the transportation system of Santiago), the national government decided to implement a battery of planning tools, including computer models, to simulate the operation of alternative network configurations and evaluate development plans. Therefore, transportation planning models were implemented in Santiago in the context of a project called “Strategic Urban Transport Study (for Santiago)” known as ESTRAUS (see SECTU 1989). This name is presently given to the supply-demand equilibrium model, which is the most important part of the Santiago model. The description of ESTRAUS, including its mathematical formulation and solution algorithm, is the main objective of this paper. The most important features of the model’s srcinal version were the following: i) The model considers a simultaneous equilibrium formulation for trip distribution, modal split and assignment, in order to ensure consistency of the levels of service in the system for the different submodels. In this way, the levels of service used to estimate demands (i.e. total trips and trips by mode among zones) must be the same as the levels of service obtained when the O/D matrices by mode are loaded over their corresponding subnetworks (road network and transit networks). ii) The trip generation stage is exogenous; that is, trip productions and attractions are given as inputs of the model. iii) The model considers multiple pure and combined (combination of pure) modes, existing in the city of Santiago. iv) The congestion interactions between all the vehicles using the road network are explicitly considered (car, taxis and vehicles offering public transport services), given that all of them compete for the same common road capacity. The exceptions are the case of the exclusive bus lanes (separate links are coded in this case), the metro lines that operate over an independent network, and the interactions of the car part of the combined mode car-passenger/metro trips with other vehicles using the road network.

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