Gabrio Caimi

A model predictive control approach for discrete-time rescheduling in complex central railway station areas

Railway networks are operated more and more at capacity margins, schedules are becoming more susceptible to disturbances, and delays propagate and hamper the service level experienced by the customers. As a consequence railway traffic management is becoming increasingly challenging, thus motivating the development of computer-aided systems. This paper proposes a dispatching assistant in the form of a model predictive control framework for a complex central railway station area. The closed-loop discrete-time system suggests rescheduling trains according to solutions of a binary linear optimization model. The model assigns precomputed blocking-stairways to trains while respecting resource-based clique constraints, connection constraints, platform related constraints and consistency constraints with the objective of maximizing customer satisfaction. In collaboration with the Swiss Federal Railways (SBB), the approach was successfully applied for an operational day at the central railway station area Berne, Switzerland. The model is capable of considering many alternative routing possibilities and departure timings, a potential of our approach, which can also be deduced from computational results.

A New Resource-Constrained Multicommodity Flow Model for Conflict-Free Train Routing and Scheduling

This paper addresses the problem of generating conflict-free train schedules on a microscopic model of the railway infrastructure. Conflicts arise if two or more trains are scheduled to block the same track section at the same time. A standard model for this problem is the so-called conflict graph, where each considered train path corresponds to a vertex, and edges represent pairwise conflicts so that a conflict-free schedule corresponds to a maximum independent set. Because the linear programming relaxation of the conflict graph formulation is typically very weak, we develop an alternative model using the sequence of resources that each train path passes, encoded in a resource tree. For each resource, we can efficiently determine the maximal conflict cliques by scanning through the blocking times of all train paths and use these cliques as strong cutting planes in an integer linear programming formulation. We show that the number of maximal conflict cliques is linear in the number of train paths, so the ILP formulation uses much fewer but stronger constraints compared to the conflict graph model. In tests with real-world data from the Swiss Federal Railways, the new Resource Tree Conflict Graph model generates for major stations within seconds, even though the underlying model contains about half a million binary variables. This corresponds to a reduction of the computation time of roughly two orders of magnitude when compared to previous approaches and thus allows us to tackle considerable larger problem instances.

The periodic service intention as a conceptual framework for generating timetables with partial periodicity

Abstract Many railway companies in Europe operate periodic timetables. Yet most timetables are not entirely periodic but have a mixture of different periodicities and many exceptions to cope with changing demand. Current approaches for automatic timetable generation are not able to deal with such partially periodic structures but consider only fully periodic inputs. We therefore introduce the periodic Service Intention (pSI) as a framework where customer-relevant information about train services can be described, including their periodicity information. We then address the problem of finding a feasible timetable that fulfills the requirements specified in a pSI without the need for manual post-processing. We solve this problem by projecting intended train runs over equivalence classes and thereby reducing the pSI to an augmented instance of periodic timetabling. Thus it is possible to use existing models for periodic scheduling, such as Periodic Event Scheduling Problem, to generate periodic timetables with partial periodicity, which are finally rolled out to obtain the desired daily schedule according to the commercial requirements of the pSI. Results for a test case from the timetable for central Switzerland in 2008 show that this approach needs only slightly longer computation time than for a fully periodic instance, but the additional time is compensated by the fact that post-processing becomes unnecessary and by the better quality of the solution. The approach is particularly well suited for offers with a strong periodicity but some irregularities, which could not be treated properly by existing methods.

Optical evidence for a magnetically driven structural transition in the spin web Cu3TeO6

Cu3TeO6 is a modest frustrated S = 1/2 spin system, which undergoes an antiferromagnetic transition at TN ~ 63 K. The antiferromagnetic spin alignment in Cu3TeO6 below TN is supposed to induce a magneto-elastic strain of the lattice. The complete absorption spectrum of Cu3TeO6 is obtained through Kramers-Kronig transformation of the optical reflectivity, measured from the far-infrared up to the ultraviolet spectral range as a function of temperature (T). Below T* ~ 50 K, we find a new mode at 208 cm−1. The spectral weight associated to this additional mode increases as (T* − T)1/2 with decreasing T below T*. The implication of the optical findings will be discussed in relation to the magnetic phase transition at TN.

Optical evidence for the proximity to a spin-density-wave metallic state in \(\mathsf{Na_{0.7}CoO_2}\)

Abstract.We present the optical properties of Na0.7CoO2 single crystals, measured over a broad spectral range as a function of temperature (T). The capability to cover the energy range from the far-infrared up to the ultraviolet allows us to perform reliable Kramers-Kronig transformation, in order to obtain the absorption spectrum (i.e., the complex optical conductivity). To the complex optical conductivity we apply the generalized Drude model, extracting the frequency dependence of the scattering rate (

Towards Automated Capacity Planning in Railways

\Gamma

Periodic railway timetabling with event flexibility

) and effective mass (m*) of the itinerant charge carriers. We find that

Design of a Railway Scheduling Model for Dense Services

\Gamma(\omega)\sim \omega

09. Periodic Railway Timetabling with Event Flexibility

at low temperatures and for

A multi-level framework for generating train schedules in highly utilised networks

\omega > T