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

Reliability and heterogeneity of railway services

Reliability is one of the key factors in transportation, both for passengers and for cargo. This paper examines reliability in public railway systems. Reliability of railway services is a complex matter, since there are many causes for disruptions and at least as many causes for delays to spread around in space and time. One way to increase the reliability is to reduce the propagation of delays due to the interdependencies between trains. In this paper we attempt to decrease these interdependencies by reducing the running time differences per track section, i.e. by creating more homogeneous timetables. Because of the complexity of railway systems, we use network wide simulation for the analysis of the alternative timetables. We report on both theoretical and practical cases. Besides a comparison of different timetables, also general timetabling principles are deduced.heterogeneity;simulation;reliability;transportation;railways

Stochastic Improvement of Cyclic Railway Timetables

Real-time railway operations are subject to stochastic disturbances. However, a railway timetable is a deterministic plan. Thus a timetable should be designed in such a way that it can cope with the stochastic disturbances as well as possible. For that purpose, a timetable usually contains time supplements in several process times and buffer times between pairs of consecutive trains. This paper describes a Stochastic Optimization Model that can be used to allocate the time supplements and the buffer times in a given timetable in such a way that the timetable becomes maximally robust against stochastic disturbances. The Stochastic Optimization Model was tested on several instances of NS Reizigers, the main operator of passenger trains in the Netherlands. Moreover, a timetable that was computed by the model was operated in practice in a timetable experiment on the so-called “Zaanlijnâ€. The results show that the average delays of trains can often be reduced significantly by applying relatively small modifications to a given timetable.Railway Timetabling;Stochastic Optimization;Robustness

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

Phase Synchronization in Railway Timetables

Timetable construction belongs to the most important optimization problems in public transport. Finding optimal or near-optimal timetables under the subsidiary conditions of minimizing travel times and other criteria is a targeted contribution to the functioning of public transport. In addition to efficiency (given, e.g., by minimal average travel times), a significant feature of a timetable is its robustness against delay propagation. Here we study the balance of efficiency and robustness in long-distance railway timetables (in particular the current long-distance railway timetable in Germany) from the perspective of synchronization, exploiting the fact that a major part of the trains run nearly periodically. We find that synchronization is highest at intermediate-sized stations. We argue that this synchronization perspective opens a new avenue towards an understanding of railway timetables by representing them as spatio-temporal phase patterns. Robustness and efficiency can then be viewed as properties of this phase pattern

Correlation entropy of synaptic input-output dynamics

The responses of synapses in the neocortex show highly stochastic and nonlinear behavior. The microscopic dynamics underlying this behavior, and its computational consequences during natural patterns of synaptic input, are not explained by conventional macroscopic models of deterministic ensemble mean dynamics. Here, we introduce the correlation entropy of the synaptic input-output map as a measure of synaptic reliability which explicitly includes the microscopic dynamics. Applying this to experimental data, we find that cortical synapses show a low-dimensional chaos driven by the natural input pattern.Comment: 7 pages, 6 Figures (7 figure files

Complex delay dynamics on railway networks: from universal laws to realistic modelling

Railways are a key infrastructure for any modern country. The reliability and resilience of this peculiar transportation system may be challenged by different shocks such as disruptions, strikes and adverse weather conditions. These events compromise the correct functioning of the system and trigger the spreading of delays into the railway network on a daily basis. Despite their importance, a general theoretical understanding of the underlying causes of these disruptions is still lacking. In this work, we analyse the Italian and German railway networks by leveraging on the train schedules and actual delay data retrieved during the year 2015. We use {these} data to infer simple statistical laws ruling the emergence of localized delays in different areas of the network and we model the spreading of these delays throughout the network by exploiting a framework inspired by epidemic spreading models. Our model offers a fast and easy tool for the preliminary assessment of the {effectiveness of} traffic handling policies, and of the railway {network} criticalities.Comment: 32 pages (with appendix), 28 Figures (with appendix), 2 Table

Deterministic networks for probabilistic computing

Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own private source of randomness, often in the form of uncorrelated external noise. However, both in vivo and in silico, the number of noise sources is limited due to space and bandwidth constraints. Hence, neurons in large networks usually need to share noise sources. Here, we show that the resulting shared-noise correlations can significantly impair the performance of stochastic network models. We demonstrate that this problem can be overcome by using deterministic recurrent neural networks as sources of uncorrelated noise, exploiting the decorrelating effect of inhibitory feedback. Consequently, even a single recurrent network of a few hundred neurons can serve as a natural noise source for large ensembles of functional networks, each comprising thousands of units. We successfully apply the proposed framework to a diverse set of binary-unit networks with different dimensionalities and entropies, as well as to a network reproducing handwritten digits with distinct predefined frequencies. Finally, we show that the same design transfers to functional networks of spiking neurons.Comment: 22 pages, 11 figure