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

Reliable routing in schedule-based transit networks

textA framework is proposed for determining the least expected cost path in a schedule-based time-expanded public transit network where travel times, and thus bus arrival and departure times at stops, are stochastic. Transfer reliability is incorporated in a label-correcting algorithm with a penalty function for the expected waiting time when transferring that reflects the likelihood of making a successful transfer. The algorithm is implemented in transit assignment on an Austin, Texas test network, using actual bus arrival and departure time distributions from vehicle location data. Assignment results are compared with those of a deterministic shortest path based on the schedule and from a calibrated transit assignment model. Simulations of the network and passenger paths are also conducted to evaluate the overall path reliability. The reliable shortest path algorithm is found to penalize transferring and provide paths with improved transfer and overall reliability. The proposed model is realistic, incorporating reliability measures from vehicle location data, and practical, given the efficient shortest path approach and application to transit assignment.Civil, Architectural, and Environmental Engineerin

Stochastic on-time arrival problem in transit networks

This article considers the stochastic on-time arrival problem in transit networks where both the travel time and the waiting time for transit services are stochastic. A specific challenge of this problem is the combinatorial solution space due to the unknown ordering of transit line arrivals. We propose a network structure appropriate to the online decision-making of a passenger, including boarding, waiting and transferring. In this framework, we design a dynamic programming algorithm that is pseudo-polynomial in the number of transit stations and travel time budget, and exponential in the number of transit lines at a station, which is a small number in practice. To reduce the search space, we propose a definition of transit line dominance, and techniques to identify dominance, which decrease the computation time by up to 90% in numerical experiments. Extensive numerical experiments are conducted on both a synthetic network and the Chicago transit network.Comment: 29 pages; 12 figures. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0

Timely Data Delivery in a Realistic Bus Network

Abstract—WiFi-enabled buses and stops may form the backbone of a metropolitan delay tolerant network, that exploits nearby communications, temporary storage at stops, and predictable bus mobility to deliver non-real time information. This paper studies the problem of how to route data from its source to its destination in order to maximize the delivery probability by a given deadline. We assume to know the bus schedule, but we take into account that randomness, due to road traffic conditions or passengers boarding and alighting, affects bus mobility. We propose a simple stochastic model for bus arrivals at stops, supported by a study of real-life traces collected in a large urban network. A succinct graph representation of this model allows us to devise an optimal (under our model) single-copy routing algorithm and then extend it to cases where several copies of the same data are permitted. Through an extensive simulation study, we compare the optimal routing algorithm with three other approaches: minimizing the expected traversal time over our graph, minimizing the number of hops a packet can travel, and a recently-proposed heuristic based on bus frequencies. Our optimal algorithm outperforms all of them, but most of the times it essentially reduces to minimizing the expected traversal time. For values of deadlines close to the expected delivery time, the multi-copy extension requires only 10 copies to reach almost the performance of the costly flooding approach. I

Data-driven optimization of bus schedules under uncertainties

Plusieurs sous-problèmes d’optimisation se posent lors de la planification des transports publics. Le problème d’itinéraires de véhicule (PIV) est l’un d’entre eux et consiste à minimiser les coûts opérationnels tout en assignant exactement un autobus par trajet planifié de sorte que le nombre d’autobus entreposé par dépôt ne dépasse pas la capacité maximale disponible. Bien que les transports publics soient sujets à plusieurs sources d’incertitude (à la fois endogènes et exogènes) pouvant engendrer des variations des temps de trajet et de la consommation d’énergie, le PIV et ses variantes sont la plupart du temps résolus de façon déterministe pour des raisons de résolubilité. Toutefois, cette hypothèse peut compromettre le respect de l’horaire établi lorsque les temps des trajets considérés sont fixes (c.-à-d. déterministes) et peut produire des solutions impliquant des politiques de gestion des batteries inadéquates lorsque la consommation d’énergie est aussi considérée comme fixe. Dans cette thèse, nous proposons une méthodologie pour mesurer la fiabilité (ou le respect de l’horaire établi) d’un service de transport public ainsi que des modèles mathématiques stochastiques et orientés données et des algorithmes de branch-and-price pour deux variantes de ce problème, à savoir le problème d’itinéraires de véhicule avec dépôts multiples (PIVDM) et le problème d’itinéraires de véhicule électrique (PIV-E). Afin d’évaluer la fiabilité, c.-à-d. la tolérance aux délais, de certains itinéraires de véhicule, nous prédisons d’abord la distribution des temps de trajet des autobus. Pour ce faire, nous comparons plusieurs modèles probabilistes selon leur capacité à prédire correctement la fonction de densité des temps de trajet des autobus sur le long terme. Ensuite, nous estimons à l'aide d'une simulation de Monte-Carlo la fiabilité des horaires d’autobus en générant des temps de trajet aléatoires à chaque itération. Nous intégrons alors le modèle probabiliste le plus approprié, celui qui est capable de prédire avec précision à la fois la véritable fonction de densité conditionnelle des temps de trajet et les retards secondaires espérés, dans nos modèles d'optimisation basés sur les données. Deuxièmement, nous introduisons un modèle pour PIVDM fiable avec des temps de trajet stochastiques. Ce problème d’optimisation bi-objectif vise à minimiser les coûts opérationnels et les pénalités associées aux retards. Un algorithme heuristique basé sur la génération de colonnes avec des sous-problèmes stochastiques est proposé pour résoudre ce problème. Cet algorithme calcule de manière dynamique les retards secondaires espérés à mesure que de nouvelles colonnes sont générées. Troisièmement, nous proposons un nouveau programme stochastique à deux étapes avec recours pour le PIVDM électrique avec des temps de trajet et des consommations d’énergie stochastiques. La politique de recours est conçue pour rétablir la faisabilité énergétique lorsque les itinéraires de véhicule produits a priori se révèlent non réalisables. Toutefois, cette flexibilité vient au prix de potentiels retards induits. Une adaptation d’un algorithme de branch-and-price est développé pour évaluer la pertinence de cette approche pour deux types d'autobus électriques à batterie disponibles sur le marché. Enfin, nous présentons un premier modèle stochastique pour le PIV-E avec dégradation de la batterie. Le modèle sous contrainte en probabilité proposé tient compte de l’incertitude de la consommation d’énergie, permettant ainsi un contrôle efficace de la dégradation de la batterie grâce au contrôle effectif de l’état de charge (EdC) moyen et l’écart de EdC. Ce modèle, combiné à l’algorithme de branch-and-price, sert d’outil pour balancer les coûts opérationnels et la dégradation de la batterie.The vehicle scheduling problem (VSP) is one of the sub-problems of public transport planning. It aims to minimize operational costs while assigning exactly one bus per timetabled trip and respecting the capacity of each depot. Even thought public transport planning is subject to various endogenous and exogenous causes of uncertainty, notably affecting travel time and energy consumption, the VSP and its variants are usually solved deterministically to address tractability issues. However, considering deterministic travel time in the VSP can compromise schedule adherence, whereas considering deterministic energy consumption in the electric VSP (E-VSP) may result in solutions with inadequate battery management. In this thesis, we propose a methodology for measuring the reliability (or schedule adherence) of public transport, along with stochastic and data-driven mathematical models and branch-and-price algorithms for two variations of this problem, namely the multi-depot vehicle scheduling problem (MDVSP) and the E-VSP. To assess the reliability of vehicle schedules in terms of their tolerance to delays, we first predict the distribution of bus travel times. We compare numerous probabilistic models for the long-term prediction of bus travel time density. Using a Monte Carlo simulation, we then estimate the reliability of bus schedules by generating random travel times at each iteration. Subsequently, we integrate the most suitable probabilistic model, capable of accurately predicting both the true conditional density function of the travel time and the expected secondary delays, into the data-driven optimization models. Second, we introduce a model for the reliable MDVSP with stochastic travel time minimizing both the operational costs and penalties associated with delays. To effectively tackle this problem, we propose a heuristic column generation-based algorithm, which incorporates stochastic pricing problems. This algorithm dynamically computes the expected secondary delays as new columns are generated. Third, we propose a new two-stage stochastic program with recourse for the electric MDVSP with stochastic travel time and energy consumption. The recourse policy aims to restore energy feasibility when a priori vehicle schedules are unfeasible, which may lead to delays. An adapted algorithm based on column generation is developed to assess the relevance of this approach for two types of commercially available battery electric buses. Finally, we present the first stochastic model for the E-VSP with battery degradation. The proposed chance-constraint model incorporates energy consumption uncertainty, allowing for effective control of battery degradation by regulating the average state-of-charge (SOC) and SoC deviation in each discharging and charging cycle. This model, in combination with a tailored branch-and-price algorithm, serves as a tool to strike a balance between operational costs and battery degradation

Optimal Pricing to Manage Electric Vehicles in Coupled Power and Transportation Networks

We study the system-level effects of the introduction of large populations of Electric Vehicles on the power and transportation networks. We assume that each EV owner solves a decision problem to pick a cost-minimizing charge and travel plan. This individual decision takes into account traffic congestion in the transportation network, affecting travel times, as well as as congestion in the power grid, resulting in spatial variations in electricity prices for battery charging. We show that this decision problem is equivalent to finding the shortest path on an "extended" transportation graph, with virtual arcs that represent charging options. Using this extended graph, we study the collective effects of a large number of EV owners individually solving this path planning problem. We propose a scheme in which independent power and transportation system operators can collaborate to manage each network towards a socially optimum operating point while keeping the operational data of each system private. We further study the optimal reserve capacity requirements for pricing in the absence of such collaboration. We showcase numerically that a lack of attention to interdependencies between the two infrastructures can have adverse operational effects.Comment: Submitted to IEEE Transactions on Control of Network Systems on June 1st 201

Smart Cities and M³: Rapid Research, Meaningful Metrics and Co-Design

The research described in this paper is undertaken under the banner of the smart city, a concept that captures the way urban spaces are re-made by the incursion of new technology. Much of smart is centred on converting everyday activities into data, and using this data to generate knowledge mediated by technology. Ordinary citizens, those that may have their lives impacted by the technology, usually are not properly involved in the ‘smartification’ process. Their perceptions, concerns and expectations should inform the conception and development of smart technologies at the same extent. How to engage general public with smart cities research is the central challenge for the Making Metrics Meaningful (MMM) project. Applying a rapid participatory method, ‘Imagine’ over a five-month period (March – July) the research sought to gain insights from the general public into novel forms of information system innovation. This brief paper describes the nature of the accelerated research undertaken and explores some of the themes which emerged in the analysis. Generic themes, beyond the remit of an explicit transport focus, are developed and pointers towards further research directions are discussed. Participatory methods, including engaging with self- selected transport users actively through both picture creation and programmatically specific musical ‘signatures’ as well as group discussion, were found to be effective in eliciting users’ own concerns, needs and ideas for novel information systems