Compact Trip Representation over Networks

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-46049-9_23[Abstract] We present a new Compact Trip Representation ( CTRCTR ) that allows us to manage users’ trips (moving objects) over networks. These could be public transportation networks (buses, subway, trains, and so on) where nodes are stations or stops, or road networks where nodes are intersections. CTRCTR represents the sequences of nodes and time instants in users’ trips. The spatial component is handled with a data structure based on the well-known Compressed Suffix Array ( CSACSA ), which provides both a compact representation and interesting indexing capabilities. We also represent the temporal component of the trips, that is, the time instants when users visit nodes in their trips. We create a sequence with these time instants, which are then self-indexed with a balanced Wavelet Matrix ( WMWM ). This gives us the ability to solve range-interval queries efficiently. We show how CTRCTR can solve relevant spatial and spatio-temporal queries over large sets of trajectories. Finally, we also provide experimental results to show the space requirements and query efficiency of CTRCTR .Ministerio de Economía y Competitividad; TIN2013-46238-C4-3-RMinisterio de Economía y Competitividad; TIN2013-47090-C3-3-PMinisterio de Economía y Competitividad; IDI-20141259Ministerio de Economía y Competitividad; ITC-20151305Ministerio de Economía y Competitividad; ITC-20151247Xunta de Galicia; GRC2013/053Chile.Fondo Nacional de Desarrollo Científico y Tecnológico; 1140428Chile. Instituto de Sistemas Complejos de Ingeniería ; FBO 1

A demand model with departure time choice for within-day dynamic traffic assignment

A within-clay dynamic demand model is formulated, embodying, in addition to the classic generation, distribution and modal split stages, an actual demand model taking into account departure time choice. The work focuses on this last stage, represented through an extension of the discrete choice framework to a continuous choice set. The dynamic multimodal supply and equilibrium model based on implicit path enumeration, which have been developed in previous work are outlined here, to define within-day dynamic elastic demand stochastic multimodal equilibrium as a fixed point problem on users flows and transit line frequencies. A MSA algorithm capable, in the case of Logit route choice models, of supplying equilibrium flows and frequencies on real dimension networks, is presented, as well as the specific procedures implementing the departure time choice and actual demand models. Finally, the results obtained on a test network are presented and conclusions are drawn. (c) 2005 Elsevier B.V. All rights reserved

An optimization model for line planning and timetabling in automated urban metro subway networks

In this paper we present a Mixed Integer Nonlinear Programming model that we developed as part of a pilot study requested by the R&D company Metrolab in order to design tools for finding solutions for line planning and timetable situations in automated urban metro subway networks. Our model incorporates important factors in public transportation systems from both, a cost-oriented and a passenger-oriented perspective, as time-dependent demands, interchange stations, short-turns and technical features of the trains in use. The incoming flows of passengers are modeled by means of piecewise linear demand functions which are parameterized in terms of arrival rates and bulk arrivals. Decisions about frequencies, train capacities, short-turning and timetables for a given planning horizon are jointly integrated to be optimized in our model. Finally, a novel Math-Heuristic approach is proposed to solve the problem. The results of extensive computational experiments are reported to show its applicability and effectiveness to handle real-world subway networksComment: 30 pages, 6 figures, 9 table

Existence of simultaneous route and departure choice dynamic user equilibrium

This paper is concerned with the existence of the simultaneous route-and-departure choice dynamic user equilibrium (SRDC-DUE) in continuous time, first formulated as an infinite-dimensional variational inequality in Friesz et al. (1993). In deriving our existence result, we employ the generalized Vickrey model (GVM) introduced in and to formulate the underlying network loading problem. As we explain, the GVM corresponds to a path delay operator that is provably strongly continuous on the Hilbert space of interest. Finally, we provide the desired SRDC-DUE existence result for general constraints relating path flows to a table of fixed trip volumes without invocation of a priori bounds on the path flows.Comment: 21 page

The influence of land use and mobility policy on travel behavior : a comparative case study of Flanders and the Netherlands

Numerous transportation studies have indicated that the local built environment can have an important effect on travel behavior; people living in suburban neighborhoods travel more by car than people living in urban neighborhoods. In this paper, however, we will analyze whether the regional land use has an important influence on travel behavior by comparing two regions with a varying land-use pattern: Flanders (Belgium) and the Netherlands. The different land-use pattern seems to have influenced travel behavior in both regions. An active spatial planning policy in the Netherlands, clustering activities in urban surroundings, appears to have realized a sustainable travel behavior, as a substantial share of residents frequently walk, cycle or use public transportation. The rather passive spatial planning in Flanders, resulting in urban sprawl, seems to stimulate car use. The applied mobility policy also has an impact on the travel behavior and land use of the Flemings and the Dutch. Infrastructure is concentrated in Dutch urban environments, whereas Flanders has a more widespread network of infrastructure and cheap public transportation, resulting in a further increase of suburbanization

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Skorokhod's M1 topology for distribution-valued processes

Skorokhod's M1 topology is defined for c\`adl\`ag paths taking values in the space of tempered distributions (more generally, in the dual of a countably Hilbertian nuclear space). Compactness and tightness characterisations are derived which allow us to study a collection of stochastic processes through their projections on the familiar space of real-valued c\`adl\`ag processes. It is shown how this topological space can be used in analysing the convergence of empirical process approximations to distribution-valued evolution equations with Dirichlet boundary conditions.Comment: 13 pages, 2 figure