Abstract: About this book
This state-of-the-art survey features papers that were selected after an open call following the International Dagstuhl Seminar on Algorithmic Methods for Railway Optimization held in Dagstuhl Castle, Germany, in June 2004. The second part of the volume constitutes the refereed proceedings of the 4th International Workshop on Algorithmic Methods and Models for Optimization of Railways held in Bergen, Norway, in September 2004.
The volume covers algorithmic methods for analyzing and solving problems arising in railway optimizations, with a special focus on the interplay between railway and other public transportation systems. Beside algorithmics and mathematical optimization, the relevance of formal models and the influence of applications on problem modeling are also considered. In addition, the papers address experimental studies and useful prototype implementations.
The 17 full papers presented here were carefully reviewed and selected from numerous submissions and are organized into topical sections covering network and line planning, timetabling and timetableinformation, rolling stock and crew scheduling, and real-time operations.
Abstract: An ever growing emphasis is put nowadays in developing personalized journey planning and renewable mobility services in smart cities. These services combine means of scheduled-based public transport and electric vehicles or bikes, using crowdsourcing techniques for collecting real-time traffic information and for assessing the recommended routes. The goal is to develop an information system that will allow the fast, real-time computation of best routes.
The main challenges in developing such an information system are both technological and algorithmic. The technological challenge concerns the collection, storage, management, and updating of a huge volume of transport data that are usually time-dependent, and the provision (through these data) of personalized renewable mobility services in smartphones. This challenge is typically confronted by creating a cloud infrastructure that on the one hand will support the storage, management, and updating of data, while on the other hand it will handle the necessary data feed to the smartphone applications for providing the users with the requested best routes.
The algorithmic challenge concerns the development of innovative algorithms for the efficient provision of journey planning services in smartphones, based on data they will receive from the cloud infrastructure. These services guarantee the computation of realistic and useful best routes, as well as the updating of the precomputed (route and timetable) information, in case of delays of scheduled public transport vehicles, so that the users can online update their routes to destination. The goal is to develop an algorithmic basis for supporting modern renewable mobility services (information systems), such as "mobility on demand'' (where the next leg of a journey is decided in real-time) and "door-to-door'' personalized mobility, in urban scheduled-based public transport environments. Scheduled-based public transport information systems should not only compute in real-time end-user queries requesting best routes, but also to update the timetableinformation in case of delays.
The core algorithmic issues of mobility and journey planning (regarding the computation of optimal routes under certain criteria) in scheduled-based public transport systems concern the efficient solution of the fundamental earlier arrival (EA) problem (compute a journey from station S to station T minimizing the overall traveling time required to complete the journey), the minimum number of
transfers (MNT) problem (compute a journey from station S to station T minimizing the number of times a passenger is required to change vehicle), and the efficient updating of timetableinformation system in case of vehicle delays. The EA and MNT problems have been extensively studied in the literature under two main approaches: the array-based modeling (where the timetable is represented as an array) and the graph-based modeling (where the timetable is represented as a graph). Experimental results have shown so far that the array-based approaches are faster in terms of query time than graph-based ones, as they are able to better exploit data locality and do not rely on priority queues. On the other hand, the array-based approaches have not been theoretically or experimentally studied as far as the efficient updating of timetableinformation, in case of delays, is concerned.
In this thesis, new graph-based models are being developed that solve efficiently the aforementioned fundamental algorithmic mobility problems in urban scheduled-based public transport information systems, along with a mobile application (journey planner) running on Android-based smartphones that includes a service for the evaluation of the recommended routes by the users. In particular:
(a) An extensive comparative evaluation was conducted on graph-based dynamic models that represent big data volumes regarding their suitability for representing timetableinformation. The study confirmed that the realistic time-expanded model is the most suitable for representing timetableinformation.
(b) Two new graph-based models have been developed for representing timetableinformation (in a timetableinformation system), the reduced time-expanded model and the dynamic timetable model (DTM), both of which are more space-efficient with respect to the realistic time-expanded model. For both of the new models, new efficient algorithms were developed for fast answering of EA and MNT queries, as well as for updating the timetableinformation representation in case of delays.
(c)An experimental evaluation was conducted with the new graph-based models and their associated query and update algorithms on a set of 14 real-world scheduled-based transportation systems, including the metropolitan areas of Berlin, Athens, London, Rome, and Madrid. The experimental results showed that the query algorithms of the reduced time-expanded model are superior to those of the DTM model, while the reverse is true regarding the update algorithms. In addition, the experimental study showed that the query algorithms of the new graph-based models compete favorably with those of the best array-based models.
(d) A mobile, cloud-based, journey planner (information system) was developed whose core algorithmic engine builds upon the new graph-based models. The mobile application is accompanied by a service that allows the users to assess the recommended journeys. The journey planner demonstrates the practicality of the new graph-based models and their associated query and update algorithms.
Abstract: We consider two approaches that model timetableinformation in public transportation systems
as shortest-path problems in weighted graphs. In the time-expanded approach, every event at
a station, e.g., the departure of a train, is modeled as a node in the graph, while in the timedependent
approach the graph contains only one node per station. Both approaches have been
recently considered for (a simplified version of) the earliest arrival problem, but little is known
about their relative performance. Thus far, there are only theoretical arguments in favor of the
time-dependent approach. In this paper, we provide the first extensive experimental comparison of
the two approaches. Using several real-world data sets, we evaluate the performance of the basic
models and of several new extensions towards realistic modeling. Furthermore, new insights on
solving bicriteria optimization problems in both models are presented. The time-expanded approach
turns out to be more robust for modeling more complex scenarios, whereas the time-dependent
approach shows a clearly better performance.
Abstract: We consider two approaches that model timetableinformation in public transportation systems
as shortest-path problems in weighted graphs. In the time-expanded approach, every event at
a station, e.g., the departure of a train, is modeled as a node in the graph, while in the timedependent
approach the graph contains only one node per station. Both approaches have been
recently considered for (a simplified version of) the earliest arrival problem, but little is known
about their relative performance. Thus far, there are only theoretical arguments in favor of the
time-dependent approach. In this paper, we provide the first extensive experimental comparison of
the two approaches. Using several real-world data sets, we evaluate the performance of the basic
models and of several new extensions towards realistic modeling. Furthermore, new insights on
solving bicriteria optimization problems in both models are presented. The time-expanded approach
turns out to be more robust for modeling more complex scenarios, whereas the time-dependent
approach shows a clearly better performance.
Abstract: We consider the Railway Traveling Salesman Problem (RTSP) in which a salesman using the railway network wishes to visit a certain number of cities to carry out his/her business, starting and ending at the same city, and having as goal to minimize the overall time of the journey. RTSP is an $\mathcal{NP}$ -hard problem. Although it is related to the Generalized Asymmetric Traveling Salesman Problem, in this paper we follow a direct approach and present a modelling of RTSP as an integer linear program based on the directed graph resulted from the timetableinformation. Since this graph can be very large, we also show how to reduce its size without sacrificing correctness. Finally, we conduct an experimental study with real-world and synthetic data that demonstrates the superiority of the size reduction approach.
Abstract: The timetableinformation problem can be solved by computing shortest paths in special graphs built from timetable data. In general, two models exist: the time-dependent and time-expanded network. In a recent work, both models are compared with respect to advantages and disadvantages on a theoretical and a practical framework. In addition, an extensive experimental evaluation reveals further differences with respect to query performance. However, delays which occur very frequently in railway systems are not covered. In this work, we show how the time-dependent and the time-expanded models should be updated in order to capture delays. It turns out that delays can be incorporated in the time-dependent model without changing the topology of the network. This is not true for the time-expanded model, whose updating involves a (sometimes large) sequence of edge insertions, deletions, and cost modifications.
Abstract: We give an overview of models and efficient algorithms for
optimally solving timetableinformation problems like “given a departure
and an arrival station as well as a departure time, which is the
connection that arrives as early as possible at the arrival station?” Two
main approaches that transform the problems into shortest path problems
are reviewed, including issues like the modeling of realistic details
(e.g., train transfers) and further optimization criteria (e.g., the number
of transfers). An important topic is also multi-criteria optimization,
where in general all attractive connections with respect to several criteria
shall be determined. Finally, we discuss the performance of the described
algorithms, which is crucial for their application in a real system.
Abstract: We give an overview of models and efficient algorithms for optimally solving timetableinformation problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transform the problems into shortest path problems are reviewed, including issues like the modeling of realistic details (e.g., train transfers) and further optimization criteria (e.g., the number of transfers). An important topic is also multi-criteria optimization, where in general all attractive connections with respect to several criteria shall be determined. Finally, we discuss the performance of the described algorithms, which is crucial for their application in a real system.
Abstract: In many fields of application, shortest path finding problems
in very large graphs arise. Scenarios where large numbers of on-line
queries for shortest paths have to be processed in real-time appear for example
in traffic information systems. In such systems, the techniques considered
to speed up the shortest path computation are usually based on
precomputed information. One approach proposed often in this context
is a space reduction, where precomputed shortest paths are replaced by
single edges with weight equal to the length of the corresponding shortest
path. In this paper, we give a first systematic experimental study of
such a space reduction approach. We introduce the concept of multi-level
graph decomposition. For one specific application scenario from the field
of timetableinformation in public transport, we perform a detailed analysis
and experimental evaluation of shortest path computations based
on multi-level graph decomposition.