The Price of Robustness in Timetable Information

In timetable information in public transport the goal is to search for a good passenger\u27s path between an origin and a destination. Usually, the travel time and the number of transfers shall be minimized. In this paper, we consider robust timetable information, i.e. we want to identify a path which will bring the passenger to the planned destination even in the case of delays. The classic notion of strict robustness leads to the problem of identifying those changing activities which will never break in any of the expected delay scenarios. We show that this is in general a strongly NP-hard problem. Therefore, we propose a conservative heuristic which identifies a large subset of these robust changing activities in polynomial time by dynamic programming and so allows us to find strictly robust paths efficiently. We also transfer the notion of light robustness, originally introduced for timetabling, to timetable information. In computational experiments we then study the price of strict and light robustness: How much longer is the travel time of a robust path than of a shortest one according to the published schedule? Based on the schedule of high-speed trains within Germany of 2011, we quantitatively explore the trade-off between the level of guaranteed robustness and the increase in travel time. Strict robustness turns out to be too conservative, while light robustness is promising: a modest level of guarantees is achievable at a reasonable price for the majority of passengers

Path Finding Strategies in Stochastic Networks

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 dynamic-programming 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

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Delay-Robust Journeys in Timetable Networks with Minimum Expected Arrival Time

We study the problem of computing delay-robust routes in timetable networks. Instead of a single path we compute a decision graph containing all stops and trains/vehicles that might be relevant. Delays are formalized using a stochastic model. We show how to compute a decision graph that minimizes the expected arrival time while bounding the latest arrival time over all sub-paths. Finally we show how the information contained within a decision graph can compactly be represented to the user. We experimentally evaluate our algorithms and show that the running times allow for interactive usage on a realistic train network

Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations

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. [Buhmann et al., ITCS 2013] 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

Kvantificering samt forbedring af robusthed og punktlighed i jernbanetransport: En gennemgang af litteraturen

I denne artikel gennemgås studier, der har beskæftiget sig med punktlighed og robusthed indenfor jernbanedrift. For disse to servicemål undersøges det hvilke definitioner og kvantificérbare mål litteraturen har benyttet sig af op til i dag. Ligeledes undersøges det også, hvilke metoder der har været anvendt til at forbedre jernbanedriften. Dette studie fremhæver forskellen mellem tog- og passagerforsinkelser samt at måden hvorpå passagerernes rutevalg er estimeret, har signifikant indflydelse på korrektheden af resultaterne når beregnede resultater sammenlignes med virkeligheden. Baseret på denne gennemgang af litteraturen foreslås slutteligt nogle retningslinjer for fremtidige perspektiver

Robust routing in urban public transportation: How to find reliable journeys based on past observations.

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

Optimizing last trains timetable in the urban rail network: social welfare and synchronization

Last train timetable design is to coordinate last train services from different lines in an urban rail network for maximizing the number of transfers. It is a challenging operational research problem to balance the competing demand of two decision agents: that of the government agencies to provide the best social services with minimal government subsidy, and that of the train operating companies to minimize operating costs. A bi-level programming model is formulated for the last train timetabling problem, in which the upper level is to maximize the social service efficiency, and the lower level is to minimize the revenue loss for the operating companies. To solve this problem, a genetic algorithm combined with an active-set approach is developed. We report the optimization results on real-world cases of the Beijing subway network. The results show that the optimized last train timetable can significantly improve the transfer coordination