Mathias Schnee

Finding all attractive train connections by multi-criteria Pareto search

We consider efficient algorithms for timetable information in public transportation systems undermultiple objectives like, for example, travel time, ticket costs, and number of interchanges between different means of transport. In this paper we focus on a fully realistic scenario in public railroad transport as it appears in practice while most previous work studied only simplified models. Algorithmically this leads to multi-criteria shortest path problems in very large graphs. With several objectives the challenge is to find all connections which are potentially attractive for customers. To meet this informal goal we introduce the notion of relaxed Pareto dominance. Another difficulty arises from the fact that due to the complicated fare regulations even the single-criteria optimization problem of finding cheapest connections is intractable. Therefore, we have to work with fare estimations during the search for good connections. In a cooperation with Deutsche Bahn Systems we realized this scenario in a prototypal implementation called PARETO based on a timeexpanded graph model. Computational experiments with our PARETO server demonstrate that the current central server of Deutsche Bahn AG often fails to give optimal recommendations for different user groups. In contrast, an important feature of the PARETO server is its ability to provide many attractive alternatives.

Efficient Timetable Information in the Presence of Delays

The search for train connections in state-of-the-art commercial timetable information systems is based on a static schedule. Unfortunately, public transportation systems suffer from delays for various reasons. Thus, dynamic changes of the planned schedule have to be taken into account. A system that has access to delay information about trains (and uses this information within search queries) can provide valid alternatives in case a connection does not work. Additionally, it can be used to actively guide passengers as these alternatives may be presented before the passenger is already stranded at a station due to an invalid transfer. In this work, we present an approach which takes a stream of delay information and schedule changes on short notice (partial train cancellations, extra trains) into account. Primary delays of trains may cause a cascade of so-called secondary delays of other trains which have to wait according to certain policies for delays between connecting trains. We introduce the concept of a dependency graph to efficiently calculate and update all primary and secondary delays. This delay information is then incorporated into a time-expanded search graph which has to be updated dynamically. These update operations are quite complex, but turn out to be not time-critical in a fully realistic scenario. We finally present a case study with data provided by Deutsche Bahn AG, showing that this approach has been successfully integrated into the multi-criteria timetable information system MOTIS and can handle massive delay data streams instantly.

Getting Train Timetables into the Main Storage

Abstract Organizing the data such that accesses to the background device are widely avoided is one of the main challenges in applications with large data sets. We present helpful experiences from an on-going project in which we develop an algorithmic kernel for a quality-assurance tool to counter-check the accuracy of customer information systems for traffic connections.

Passenger flow-oriented train disposition

Disposition management solves the decision problem whether a train should wait for incoming delayed trains or not. This problem has a highly dynamic nature due to a steady stream of update information about delayed trains. A dispatcher has to solve a global optimization problem since his decisions have an effect on the whole network, but he takes only local decisions for subnetworks (for few stations and only for departure events in the near future). In this paper, we introduce a new model for an optimization tool. Our implementation includes as building blocks (1) routines for the permanent update of our graph model subject to incoming delay messages, (2) routines for forecasting future arrival and departure times, (3) the update of passenger flows subject to several rerouting strategies (including dynamic shortest path queries), and (4) the simulation of passenger flows. The general objective is the satisfaction of passengers. We propose three different formalizations of objective functions to capture this goal. Experiments on test data with the train schedule of German Railways and real delay messages show that our disposition tool can compute waiting decisions within a few seconds. In a test with artificial passenger flows it is fast enough to handle the typical amount of decisions which have to be taken within a period of 15 minutes in real time.

Reliability and Delay Distributions of Train Connections

Finding reliable train connections is a considerable issue in timetable information since train delays perturb the timetable daily. We present an effective probabilistic approach for estimating the reliability of connections in a large train network. Experiments on real customer queries and real timetables for all trains in Germany show that our approach can be implemented to deliver good results at the expense of only little processing time. Based on probability distributions for train events in connections, we estimate the reliability of connections. We have analyzed our computed reliability ratings by validating our predictions against real delay data from German Railways. This study shows that we are able to predict the feasibility of connections very well. In essence, our predictions are slightly optimistic for connections with a high rating and pretty accurate for connections with a medium rating. Only for the rare cases of a very low rating, we are too pessimistic. Our probabilistic approach already delivers good results, still has improvement potential, and offers a new perspective in the search for more reliable connections in order to bring passengers safely to their destinations even in case of delays.

Distributed Graph-based Topology Adaptation using Motif Signatures.

A motif is a small graph pattern, and a motif signature counts the occurrences of selected motifs in a network. The motif signature of a real-world network is an important characteristic because it is closely related to a variety of semantic and functional aspects. In recent years, motif analysis has been successfully applied for adapting topologies of communication networks: The motif signatures of very good networks (e.g., in terms of load balancing) are determined a priori to derive a target motif signature. Then, a given network is adapted in iterative steps, subject to side constraints and in a distributed way, such that its motif signature approximates the target motif signature. In this paper, we formalize this adaptation problem and show that it is N P-hard. We present LoMbA, a generic approach for motif-based graph adaptation: All types of networks, all selections of motifs, and all types of consistency-maintaining constraints can be incorporated. To evaluate LoMbA, we conduct a simulation study based on several scenarios of topology adaptation from the domain of communication networks. We consider topology control in wireless ad-hoc networks, balancing of video streaming trees, and load balancing of peer-to-peer overlays. In each considered application scenario, the simulation results are remarkably good, although the implementation was not tuned toward these scenarios.

How to find good night train connections

The search for attractive night train connections is fundamentally different from ordinary search: the primary objective of a customer of a night train is to have a reasonably long sleeping period without interruptions due to train changes. For most passengers it is also undesirable to reach the final destination too early in the morning. These objectives are in sharp contrast to standard information systems which focus on minimizing the total travel time. In this article, we present and compare two new approaches to support queries for night train connections. These approaches have been integrated into the Multi-Objective Traffic Information System (MOTIS), which is currently being developed by our group. Its purpose is to find all train connections which are attractive from a customer point of view. Using a computational study, we demonstrate that our specialized algorithms for night train connections are able to satisfy customer queries much better than standard methods. This can be achieved with reasonable computational costs: a specialized night train search requires only a few seconds of CPU time.

Arrive in Time by Train with High Probability

Very often, a train passenger must meet a deadline at the destination, for example, to catch a plane or to arrive at an important meeting on time. Train delays and broken connections let the passenger arrive later than scheduled. Events of this kind are usually not foreseeable before the journey commences. To be on the safe side, a connection should be prebooked such that, in case the connection breaks anywhere, alternative continuations guarantee arrival prior to the deadline with acceptably high probability. For busy people, the challenge is to commence the journey as late as possible, provided the risk of failing to meet the deadline is negligible. This scenario translates into the problem to find the latest connection plus alternative continuations such that the probability of meeting the deadline is not lower than a given required probability of success (close to 100%). We present a dynamic-programming approach to this optimization problem and report on an empirical study based on comprehensive real-...

Evaluation study for clustering in wireless sensor networks

Typically, wireless sensor nodes are battery-powered. The networks lifetime depends on the energy consumption of the sensor nodes. Transmitting messages causes a good portion of this energy consumption. Clustering the sensor nodes may reduce energy consumption through local communication and aggregation. Many clustering algorithms exist, but corresponding simulation results are hardly comparable. This paper conducts an extensive simulation study. We compare five popular clustering algorithms in four different scenarios under strictly uniform conditions. Our results indicate that two criteria for clustering algorithms are particularly important: considering residual energy for cluster head selection, and small communication overhead during cluster formation.