A variational inequality reformulation of a congested transit assignment model by Cominetti, Correa, Cepeda, and Florian

In the paper by Cominetti and Correa (2001) [Common-lines and passenger assignment in congested transit networks. Transportation Science 35 (3), pp 250-267], an extension to the common-lines problem for general multidestination networks under congestion is analyzed. Their transit equilibrium assignment model allows for a full representation of congestion effects caused by the variation of effective frequencies experienced by passengers at transit stops. This model is the first to address these characteristics consistently with the concept of strategies. In a subsequent paper by Cepeda et al. (2006) [Cepeda, M., Cominetti, and R. Florian, M. (2006) A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria. Trans. Res B 40, 437-459], the computation of equilibrium is performed heuristically by the minimization of a gap function, using the method of successive averages. In this paper, a reformulation of this congested transit equilibrium assignment model is performed, demonstrating that the problem can be expressed as an equivalent variational inequality. The case of strictly capacitated transit networks is explored under the scope of this new reformulation, and new, broader conditions for the existence of solutions to this congested transit assignment model are determined.Peer ReviewedPostprint (published version

A dynamic estimation of passenger OD matrices based on space-state models

Dynamic OD passenger matrices must be taken into account when designing robust public transport systems. The adjustment of these matrices is examined using passenger counts provided by a space-state model formulation in a demand-variable peak-period. The Kalman filter approach also incorporates ICT data, based on the detection of the electronic signature of on-board devices, thus providing a rich source of data that can be used in space-state models to simplify its formulation. It reduces the dimension of the state vector and allows a linear mapping between state variables and measurements.Peer ReviewedPostprint (author’s final draft

A computational comparison of two simplicial decomposition approaches for the separable traffic assignment problems : RSDTA and RSDVI

Draft pel 4th Meeting del Euro Working Group on Transportation (Newcastle 9-11 setembre de 1.996)The class of simplicial decomposition methods has shown to constitute efficient tools for the solution of the variational inequality formulation of the general traffic assignment problem. The paper presents a particular implementation of such an algorithm, called RSDVI, and a restricted simplicial decomposition algorithm, developed adhoc for diagonal, separable, problems named RSDTA. Both computer codes are compared for large scale separable traffic assignment problems. Some meaningful figures are shown for general problems with several levels of asymmetry.Preprin

The general traffic assignment problem: a proximal point method for equilibrium computation with applications to the demand adjustment problem

An adaptation of the proximal algorithm for the traffic assignment problem under a user equilibrium formulation for a general asymmetric traffic network is presented in this paper. It follows the recently published results of Pennanen regarding convergence under non monotonicity. As it is well known the problem can be formulated as a variational inequality and the algorithmic solutions developed up to date guarantee convergence only under too restrictive conditions which are difficult to appear in practice. In this paper it is also discussed the possibility of including the algorithm on a demand adjustment problem formulated as a bilevel program with lower level traffic equilibrium constraints expressed as a variational inequality.Peer ReviewedPostprint (published version

Dynamic OD transit matrix estimation: formulation and model-building environment

The aim of this paper is to provide a detailed description of a framework for the estimation of time-sliced origin-destination (OD) trip matrices in a transit network using counts and travel time data of Bluetooth Smartphone devices carried by passengers at equipped transit-stops. A Kalman filtering formulation defined by the authors has been included in the application. The definition of the input for building the space-state model is linked to network scenarios modeled with the transportation planning platform EMME. The transit assignment framework is optimal strategy-based, which determines the subset of paths related to the optimal strategies between all OD pairsPeer ReviewedPostprint (author’s final draft

Diseño de Servicios Auxiliares de Líneas de autobuses en interrupciones de metro y cercanías

En la ponencia se aborda el problema del soporte de líneas auxiliares de autobús en el caso de interrupción de servicio de los servicios de metro y de trenes de cercanías en redes de transporte de ámbito urbano y/o metropolitano. Las líneas de metro y de cercanías permiten transportar enormes cantidades de viajeros en las áreas metropolitanas y en las grandes ciudades de forma efectiva y sostenible medioambientalmente. De hecho, constituyen la columna vertebral del sistema de transporte urbano y posibilitan una gran parte de las actividades humanas en estos entornos. Es por tanto así que la confianza de los usuarios en estos sistemas de transporte resulta clave tanto para la economía como para la sostenibilidad y que un factor clave para el sostenimiento de dicha confianza es la regularidad de estos servicios de transporte

A heuristic method for a congested capacitated transit assignment model with strategies

This paper addresses the problem of solving the congested transit assignment problem with strict capacities. The model under consideration is the extension made by Cominetti and Correa (2001), for which the only solution method capable of resolving large transit networks is the one proposed by Cepeda et al. (2006). This transit assignment model was recently formulated by the authors as both a variational inequality problem and a fixed point inclusion problem. As a consequence of these results, this paper proposes an algo- rithm for solving the congested transit assignment problem with strict line capacities. The proposed method consists of using an MSA-based heuristic for finding a solution for the fixed point inclusion formulation. Additionally, it offers the advantage of always obtain- ing capacity-feasible flows with equal computational performance in cases of moderate congestion and with greater computational performance in cases of highly congested net- works. A set of computational tests on realistic small- and large-scale transit networks un- der various congestion levels are reported, and the characteristics of the proposed method are analyzed.Peer ReviewedPostprint (author's final draft

A model for setting services on auxiliary bus lines under congestion

In this paper, a mathematical programming model and a heuristically derived solution is described to assist with the efficient planning of services for a set of auxiliary bus lines (a bus-bridging system) during disruptions of metro and rapid transit lines. The model can be considered static and takes into account the average flows of passengers over a given period of time (i.e., the peak morning traffic hour) Auxiliary bus services must accommodate very high demand levels, and the model presented is able to take into account the operation of a bus-bridging system under congested conditions. A general analysis of the congestion in public transportation lines is presented, and the results are applied to the design of a bus-bridging system. A nonlinear integer mathematical programming model and a suitable approximation of this model are then formulated. This approximated model can be solved by a heuristic procedure that has been shown to be computationally viable. The output of the model is as follows: (a) the number of bus units to assign to each of the candidate lines of the bus-bridging system; (b) the routes to be followed by users passengers of each of the origin–destination pairs; (c) the operational conditions of the components of the bus-bridging system, including the passenger load of each of the line segments, the degree of saturation of the bus stops relative to their bus input flows, the bus service times at bus stops and the passenger waiting times at bus stops. The model is able to take into account bounds with regard to the maximum number of passengers waiting at bus stops and the space available at bus stops for the queueing of bus units. This paper demonstrates the applicability of the model with two realistic test cases: a railway corridor in Madrid and a metro line in Barcelona Planificación de los servicios de lineas auxiliares de autobuses durante las incidencias de las redes de metro y cercanías. El modelo estudia el problema bajo condiciones de alta demanda y condiciones de congestión. El modelo no lineal resultante es resuelto mediante heurísticas que demuestran su utilidad. Se demuestran los resultados en dos corredores de las ciudades de Barcelona y Madrid

Modeling and optimization of frequencies on congested bus lines

In this paper some mathematical programming models are exposed in order to set the number of services on a specified system of bus lines, which are intended to assist high demand levels which may arise because of the disruption of Rapid Transit services or during the celebration of massive events. By means of this model two types of basic magnitudes can be determined, basically: a) the number of bus units assigned to each line and b) the number of services that should be assigned to those units. In these models, passenger flow assignment to lines can be considered of the system optimum type, in the sense that the assignment of units and of services is carried out minimizing a linear combination of operation costs and total travel time of users. The models consider delays experienced by buses as a consequence of the get in/out of the passengers, queueing at stations and the delays that passengers experience waiting at the stations. For the case of a congested strategy based user optimal passenger assignment model with strict capacities on the bus lines, the use of the method of successive averages is shown

A bilevel programming formulation for modelling the location of information: points for traffic conditions

Postprint (author's final draft