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Robust routing in urban public transportation: How to find reliable journeys based on past observations.
 In ATMOS,
, 2013
"... Abstract We study the problem of robust routing in urban public transportation networks. In order to propose solutions that are robust for typical delays, we assume that we have past observations of real traffic situations available. In particular, we assume that we have "daily records" c ..."
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Abstract We study the problem of robust routing in urban public transportation networks. In order to propose solutions that are robust for typical delays, we assume that we have past observations of real traffic situations available. In particular, we assume that we have "daily records" containing the observed travel times in the whole network for a few past days. We introduce a new concept to express a solution that is feasible in any record of a given public transportation network. We adapt the method of Buhmann et al. ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems, G.2.2 Graph Theory (Graph algorithms, Network problems), I.2.6 Learning Keywords and phrases Introduction We study the problem of routing in urban public transportation networks, such as tram and bus networks in large cities, focusing on the omnipresent uncertain situations when (typical) delays occur. In particular, we search for robust routes that allow reliable yet quick passenger transportation. We think of a "dense" tram network in a large city containing many tram lines, where each tram line is a sequence of stops that is served repeatedly during the day, and where there are several options to get from one location to another. Such a network usually does not contain clear hierarchical structure (as opposed to train networks), and each line is served with high frequency. Given two tram stops a and b together with a latest arrival time t A , our goal is to provide a simple yet robust description of how to travel in the *
Is Timetabling Routing Always Reliable for Public Transport?
, 2013
"... Current route planning algorithms for public transport networks are mostly based on timetable information only, i.e., they compute shortest routes under the assumption that all transit vehicles (e.g., buses, subway trains) will incur in no delays throughout their trips. Unfortunately, unavoidable an ..."
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Current route planning algorithms for public transport networks are mostly based on timetable information only, i.e., they compute shortest routes under the assumption that all transit vehicles (e.g., buses, subway trains) will incur in no delays throughout their trips. Unfortunately, unavoidable and unexpected delays often prevent transit vehicles to respect their originally planned schedule. In this paper, we try to measure empirically the quality of the solutions offered by timetabling routing in a real public transport network, where unpredictable delays may happen with a certain frequency, such as the public transport network of the metropolitan area of Rome. To accomplish this task, we take the time estimates required for trips provided by a timetablingbased route planner (such as Google Transit) and compare them against the times taken by the trips according to the actual tracking of transit vehicles in the transport network, measured through the GPS data made available by the transit agency. In our experiments, the movement of transit vehicles was only mildly correlated to the timetable, giving strong evidence that in such a case timetabled routing may fail to deliver optimal or even highquality solutions.
DelayRobustness of Transfer Patterns in Public Transportation Route Planning ∗
, 2013
"... Transfer pattern routing is a stateoftheart speedup technique for finding optimal paths which minimize multiple cost criteria in public transportation networks. It precomputes sequences of transfer stations along optimal paths. At query time, the optimal paths are searched among the stored trans ..."
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Transfer pattern routing is a stateoftheart speedup technique for finding optimal paths which minimize multiple cost criteria in public transportation networks. It precomputes sequences of transfer stations along optimal paths. At query time, the optimal paths are searched among the stored transfer patterns, which allows for very fast response times even on very large networks. On the other hand, even a minor change to the timetables may affect many optimal paths, so that, in principle, a new computation of all optimal transfer patterns becomes necessary. In this paper, we examine the robustness of transfer pattern routing towards delay, which is the most common source of such updates. The intuition is that the deviating paths caused by typical updates are already covered by original transfer patterns. We perform experiments which show that the transfer patterns are remarkably robust even to large and many delays, which underlines the applicability and reliability of transfer pattern routing in realistic routing applications.
How to Find Reliable Journeys Based on Past Observations
, 2013
"... We study the problem of robust routing in urban public transportation networks. In order to propose solutions that are robust for typical delays, we assume that we have past observations of real traffic situations available. In particular, we assume that we have “daily records” containing the observ ..."
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We study the problem of robust routing in urban public transportation networks. In order to propose solutions that are robust for typical delays, we assume that we have past observations of real traffic situations available. In particular, we assume that we have “daily records” containing the observed travel times in the whole network for a few past days. We introduce a new concept to express a solution that is feasible in any record of a given public transportation network. We adapt the method of Buhmann et al. [4] for optimization under uncertainty, and develop algorithms that allow its application for finding a robust journey from a given source to a given destination. The performance of the algorithms and the quality of the predicted journey are evaluated in a preliminary experimental study. We furthermore introduce a measure of reliability of a given journey, and develop algorithms for its computation. The robust routing concepts presented in this work are suited specially for public transportation networks of large cities that lack clear hierarchical structure and contain services that run with high frequencies.
Engineering GraphBased Models for Dynamic Timetable Information Systems∗
"... Many efforts have been done in the last years to model public transport timetables in order to find optimal routes. The proposed models can be classified into two types: those representing the timetable as an array, and those representing it as a graph. The arraybased models have been shown to be v ..."
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Many efforts have been done in the last years to model public transport timetables in order to find optimal routes. The proposed models can be classified into two types: those representing the timetable as an array, and those representing it as a graph. The arraybased models have been shown to be very effective in terms of query time, while the graphbased models usually answer queries by computing shortest paths, and hence they are suitable to be used in combination with speedup techniques developed for road networks. In this paper, we focus on the dynamic behavior of graphbased models considering the case where transportation systems are subject to delays with respect to the given timetable. We make three contributions: (i) we give a simplified and optimized update routine for the wellknown timeexpanded model along with an engineered query algorithm; (ii) we propose a new graphbased model tailored for handling dynamic updates; (iii) we assess the effectiveness of the proposed models and algorithms by an experimental study, which shows that both models require negligible update time and a query time which is comparable to that required by some arraybased models.
Shortest Path with Alternatives for Uniform Arrival Times: Algorithms and Experiments
, 2014
"... The Shortest Path with Alternatives (SPA) policy differs from classical shortest path routing in the following way: instead of providing an exact list of means of transportation to follow, this policy gives such a list for each stop, and the traveler is supposed to pick the first option from this l ..."
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The Shortest Path with Alternatives (SPA) policy differs from classical shortest path routing in the following way: instead of providing an exact list of means of transportation to follow, this policy gives such a list for each stop, and the traveler is supposed to pick the first option from this list when waiting at some stop. First, we show that an optimal such policy can be computed in polynomial time for uniform arrival times under reasonable assumptions. A similar result was so far only known for Poisson arrival times, which are less realistic for frequencybased public transportation systems. Second, we experimentally evaluate such policies. In this context, our main finding is that SPA policies are surprisingly competitive compared to traditional shortest paths, and moreover yield a significant reduction of waiting times, and therefore improvement of user experience, compared to similar greedy approaches. Specifically, for roughly 25 % of considered cases, we could decrease the expected waiting time by at least 20%. To run our experiments, we also describe a toolchain to derive the necessary information from the popular GTFSformat, therefore allowing the application of SPA policies to a wide range of public transportation systems.
Path Finding Strategies in Stochastic Networks *
"... Abstract We introduce a novel generic algorithmic problem in directed acyclic graphs, motivated by our train delay research. Roughly speaking, an arc is admissible or not subject to the value of a random variable at its tail node. The core problem is to precompute data such that a walk along admiss ..."
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Abstract We introduce a novel generic algorithmic problem in directed acyclic graphs, motivated by our train delay research. Roughly speaking, an arc is admissible or not subject to the value of a random variable at its tail node. The core problem is to precompute data such that a walk along admissible arcs will lead to one of the target nodes with a high probability. In the motivating application scenario, this means to meet an appointment with a high chance even if train connections are broken due to train delays. We present an efficient dynamicprogramming algorithm for the generic case. The algorithm allows us to maximize the probability of success or, alternatively, optimize other criteria subject to a guaranteed probability of success. Moreover, we customize this algorithm to the application scenario. For this scenario, we present computational results based on real data from the national German railway company. The results demonstrate that our approach is superior to the natural approach, that is, to find a fast and convenient connection and to identify alternative routes for all tight train changes where the probability that the change breaks due to delays is not negligible.
Intermodal public transit routing using Linked Connections
"... Abstract. Ever since public transit agencies have found their way to the Web, they inform travelers using route planning software made available on their website. These travelers also need to be informed about other modes of transport, for which they have to consult other websites, or for which the ..."
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Abstract. Ever since public transit agencies have found their way to the Web, they inform travelers using route planning software made available on their website. These travelers also need to be informed about other modes of transport, for which they have to consult other websites, or for which they have to ask the transit agency's server maintainer to implement new functionalities. In this demo, we introduce an affordable publishing method for transit data, called Linked Connections, that can be used for intermodal route planning, by allowing user agents to execute the route planning algorithm. We publish paged documents containing a stream of hops between transit stops sorted by departure time. Using these documents, clients are able to perform intermodal route planning in a reasonable time. Furthermore, such clients are fully in charge of the algorithm, and can now also route in different ways by integrating datasets of a user's choice. When visiting our demo, conference attendees will be able to calculate intermodal routes by querying the Web of data using their phone's browser, without expensive server infrastructure.