Simultaneous Network Line Planning and Traffic Assignment

One of the basic problems in strategic planning of public and rail transport is the line planning problem to find a system of lines and its associated frequencies. The objectives of this planning process are usually manifold and often contradicting. The transport operator wants to minimize cost, whereas passengers want to have travel time shortest routes without any or only few changings between different lines. The travel quality of a passenger route depends on the travel time and on the number of necessary changings between lines and is usually measured by a disutility or impedance function. In practice the disutility strongly depends on the line plan, which is not known, but should be calculated. The presented model combines line planning models and traffic assignment model to overcome this dilemma. Results with data of Berlin\u27s city public transportion network are reported

Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations

In the last 15 years periodic timetable problems have found much interest in the combinatorial optimization community. We will focus on the optimisation task to minimise a weighted sum of undesirable slack times. This problem can be formulated as a mixed integer linear problem, which for real world instances is hard to solve. This is mainly caused by the integer variables, the so-called modulo parameter. At first we will discuss some results on the polyhedral structure of the periodic timetable problem. These ideas allow to define a modulo simplex basic solution by calculating the basic variables from modulo equations. This leads to a modulo network simplex method, which iteratively improves the solution by changing the simplex basis

Integrating Passengers\u27 Routes in Periodic Timetabling: A SAT approach

The periodic event scheduling problem (PESP) is a well studied problem known as intrinsically hard. Its main application is for designing periodic timetables in public transportation. To this end, the passengers\u27 paths are required as input data. This is a drawback since the final paths which are used by the passengers depend on the timetable to be designed. Including the passengers\u27 routing in the PESP hence improves the quality of the resulting timetables. However, this makes PESP even harder. Formulating the PESP as satisfiability problem and using SAT solvers for its solution has been shown to be a highly promising approach. The goal of this paper is to exploit if SAT solvers can also be used for the problem of integrated timetabling and passenger routing. In our model of the integrated problem we distribute origin-destination (OD) pairs temporally through the network by using time-slices in order to make the resulting model more realistic. We present a formulation of this integrated problem as integer program which we are able to transform to a satisfiability problem. We tested the latter formulation within numerical experiments, which are performed on Germany\u27s long-distance passenger railway network. The computation\u27s analysis in which we compare the integrated approach with the traditional one with fixed passengers\u27 weights, show promising results for future scientific investigations

Solving the Train Dispatching Problem in Large Networks by Column Generation

Disruptions in the operational flow of rail traffic can lead to conflicts between train movements, such that a scheduled timetable can no longer be realised. This is where dispatching is applied, existing conflicts are resolved and a dispatching timetable is provided. In the process, train paths are varied in their spatio-temporal course. This is called the train dispatching problem (TDP), which consists of selecting conflict-free train paths with minimum delay. Starting from a path-oriented formulation of the TDP, a binary linear decision model is introduced. For each possible train path, a binary decision variable indicates whether the train path is used by the request or not. Such a train path is constructed from a set of predefined path parts (\profiles{}) within a time-space network. Instead of modelling pairwise conflicts, stronger MIP formulation are achieved by a clique formulation. The combinatorics of speed profiles and different departure times results in a large number of possible train paths, so that the column generation method is used here. New train paths within the pricing-problem can be calculated using shortest path techniques. Here, the shadow prices of conflict cliques must be taken into account. When constructing a new train path, it must be determined whether this train path belongs to a clique or not. This problem is tackled by a MIP. The methodology is tested on practical size instances from a dispatching area in Germany. Numerical results show that the presented method achieves acceptable computation times with good solution quality while meeting the requirements for real-time dispatching.Comment: 12 pages, 4 figures, 2 table

Probe eines Hülfsbuchs für den deutschen Unterricht zum Gebrauch der oberen Klassen einer Realschule II. Ordnung

von Carl NachtigallProgr.-Nr. 39

Settlement characteristics of quartz grains on certain sediment surface forms of tidal beaches along the Baltic and Wadden Sea

Sind in einem Sediment, das unter dem Einfluß einer Strömung abgelagert wurde, richtungsanzeigende Indikatoren vorhanden, so werden sie je nach den momentanen Bedingungen, die zur Zeit der Sedimentation herrschten, ein mehr oder weniger gutes Abbild der Strömungsverhältnisse liefern. Zahlreich sind Strömungsanzeiger organischen Ursprungs, wie z. B. Molluskenschalen u. a. Doch auch anorganische Partikel in Psephiten und Psammiten lassen häufig in ihrer Lagerung eine Abhängigkeit von der Strömungsrichtung erkennen: sie sind "geregelt". Die Autoren der verschiedenen Arbeiten, in denen Regelungen in klastischen Sedimenten untersucht wurden, gingen von der Tatsache aus, daß viele Sedimentpartikel statistisch gesehen keine Kugelform, sondern eine längliche Gestalt besitzen. Die langen Achsen dieser länglich geformten Sedimentkörner werden im folgenden als "Langachsen" bezeichnet. In Sanden sind es vor allem Quarzkörner von annähernd zylindrischer oder ellipsoidischer Form ("Langquarze"), die geeignet sind, durch die Lage ihrer Langachsen strömungsbedingte Regelungen anzuzeigen. Mit der Orientierung solcher Langquarze in marinen und fluviatilen Sanden haben sich bisher vorwiegend amerikanische Autoren befaßt. So untersuchten z. B. Dapples & Rominger (1945) die Sandsohle eines künstlichen Gerinnes. Sie stellten fest, daß die Hauptorientierungsrichtung der Langquarze mit der Strömungsrichtung des fließenden Wassers zusammenfiel. Dabei zeigte das spitze Ende tropfenförmiger ("polarer") Quarze stromab und das stumpfe Ende stromauf. Nanz (1955) maß die Langachsenrichtungen von Langquarzen in Sanden des nassen und trockenen Strandes von Texas und Florida und fand, daß sich diese Achsen vorwiegend parallel zur Auf- und Ablaufrichtung der Wellen und damit senkrecht zum Streichen der Strandlinie einregeln. Curray (1956 b) beobachtete die gleiche Regelung. Er wies ferner darauf hin, daß in Strandwällen und Strandhaken die bevorzugte Richtung der Langquarze senkrecht zum Streichen des Sedimentkörpers liegt. Zahlreiche weitere Autoren beschäftigten sich ebenfalls mit den Fragen der Langquarzregelung, so Schwarzacher (1951), Griffith & Rosenfeld (1953), Vollbrecht (1953), Rusnak (1956), Wendler (1956), Sriramadas (1957). Ganz allgemein war das Ergebnis aller dieser Untersuchungen, daß die aus einer Strömung abgelagerten Langquarze eine Regelung parallel zur Strömungsrichtung zeigen. Eigene Untersuchungen und Überlegungen ergaben, daß die bisher veröffentlichten Ergebnisse und die an sie angeschlossenen Vorstellungen z. T. bestätigt werden können, jedoch z. T. auch erheblich modifiziert werden müssen

Die Berücksichtigung des volkswirtschaftlichen Elementes bei dem Geschichtsunterricht in höheren Lehranstalten

von NachtigallProgr.-Nr. 43