Planning a Public Transportation System with a View Towards Passengers’ Convenience by Jonas Harbering Planning a Public Transportation System with a View Towards Passengers’ Convenience Dissertation zur Erlangung des mathematisch-naturwissenschaftlichen Doktorgrades ”Doctor rerum naturalium” der Georg-August-Universit¨atG¨ottingen im Promotionsprogramm ”PhD School of Mathematical Sciences” (SMS) der Georg-August University School of Science (GAUSS) vorgelegt von Jonas Harbering aus Flemhude G¨ottingen,2015 Betreuungsausschuss Prof. Dr. Anita Sch¨obel, Institut f¨urNumerische und Angewandte Mathematik, Georg- August-Universit¨atG¨ottingen Prof. Dr. Stephan Westphal, Institut f¨urAngewandte Stochastik und Operations Research, Technische Universit¨atClausthal Mitglieder der Pr¨ufungskommision Referentin: Prof. Dr. Anita Sch¨obel, Institut f¨urNumerische und Angewandte Mathe- matik, Georg-August-Universit¨atG¨ottingen Koreferent: Prof. Dr. Juan Antonio Mesa, Institut f¨urAngewandte Mathematik, Univer- sit¨atSevilla Weitere Mitglieder der Pr¨ufungskommision Prof. Dr. Stephan Westphal, Institut f¨urAngewandte Stochastik und Operations Research, Technische Universit¨atClausthal Prof. Dr. Andrea Krajina, Institut f¨urMathematische Stochastik, Georg-August-Universit¨at G¨ottingen Prof. Dr. Preda Mihailescu, Mathematisches Institut, Georg-August-Universit¨atG¨ottingen Prof. Dr. Jens Grabowski, Institut f¨urInformatik, Georg-August-Universit¨atG¨ottingen Tag der m¨undlichen Pr¨ufung: 1. Februar 2016 ii Contents 1. Introduction 1 2. General Literature Overview 5 2.1 Network Design........................................ 7 2.2 Line Planning......................................... 9 2.3 Timetabling.......................................... 11 2.4 Delay Management...................................... 13 3. Paper Summaries 15 3.1 Minimizing the passengers’ traveling time in the stop location problem......... 16 by E. Carrizosa, J. Harbering, A. Sch¨obel Published at ATMOS 2013 Proceedings, 14 pages paper Revision submitted to the Journal of Operational Research Society, 24 pages paper 3.2 Generation of Line Pools .................................. 20 by P. Gattermann, J. Harbering, A. Sch¨obel Published at CASPT 2015 Proceedings, 17 pages paper Submitted to the journal Public Transport, 20 pages paper 3.3 Delay Resistant Line Planning with a View Towards Passenger Transfers . 23 by J. Harbering Revision submitted to the Journal of Transportation and Logistics, 21 pages paper 3.4 Single Track Train Scheduling................................ 28 by J. Harbering, A. Ranade, M. Schmidt, O. Sinnen Published at MISTA 2015 Proceedings, 16 pages paper Submitted to Journal of Scheduling, 20 pages paper 3.5 Network-based Source Detection for Propagation Processes on Complex Networks with Application to Train Delays on Railway Systems .................... 34 by J. Manitz, J. Harbering, M. Schmidt, T. Kneib, A. Sch¨obel Published at IWSM 2014 Proceedings, 5 pages paper Submitted to the Journal of the Royal Statistical Society: Series C, 48 pages paper 4. Discussion of Results 39 5. Conclusion and Future Work 43 6. Own Contribution 45 Bibliography 46 Addenda 57 Addendum A: Minimizing the passengers’ traveling time in the stop location problem . 57 Addendum B: Generation of Line Pools ............................ 91 Addendum C: Delay Resistant Line Planning with a View Towards Passenger Transfers . 119 Addendum D: Single Track Train Scheduling .........................151 Addendum E: Network-based Source Detection for Propagation Processes on Complex Networks with Application to Train Delays on Railway Systems . 177 iii 1. Introduction Public transportation is increasingly used by passengers. Ever more people intend to travel on longer distances using public transportation. The consequence for operators is that they have to provide sufficient capacity in order to satisfy passengers’ demand. How- ever, public transportation operators are facing difficulties as costs are also increasing. Examples for influencing cost factors are labor wages and energy consumption. Statistics on public transportation demand and influencing cost factors are provided by [Eur15]. Finally, also political goals are embodied in this topic. As public transportation is con- sidered to be safer and more sustainable than, e.g., private transportation, (see [Ban08]) there is a political will to support public transportation usage [OEC15]. In order to provide a guidance on how to deal with the difficulties and how to achieve efficiency goals, an intergovernmental organization, the ”International Transportation Fo- rum”, consisting of 57 member countries, was created in 2006. The forum describes their aim ”to foster a deeper understanding of the role of transportation in economic growth, environmental sustainability and social inclusion and to raise the public profile of trans- portation policy” (see [ITF15]). As such, they are regularly publishing discussion papers stating the role of current and future research areas. Two recent papers are concerned with the improvement of railways, emphasizing on crucial factors from the operators’ perspective ([MBP15]) and from passengers’ view ([WAC+14]). In [MBP15] the efficiency aspect of railway operators is further analyzed, stating that key indicators are, among others, passenger transportation operators’ revenue to cost ratio, infrastructure managers’ revenue to cost ratio, utilization of railway infrastructure, and utilization of freight/passenger transportation operators. Putting this differently, important values for both freight and passenger transportation operators are: generalized costs including, e.g., marketing costs, labor costs, train operating costs, • and maintenance costs of fleet and infrastructure, revenue from passengers or companies transporting freight or demanding freight • 1 transport, and utilization of freight and passenger train capacity. • See [MBP15] for a more detailed analysis of efficiency indicators. This thesis is mainly concerned with problems arising in the area of passenger transport. Elaborating on passengers’ perception of railway services, [WAC+14] reviews the key factors of the convenience of passengers, or short passenger convenience. The elements found to compose the convenience perception of passengers are: Accessibility, described by access and egress time. Also the walking time during the • journey is embodied in this element. Time spent waiting at any stage of the journey. • Availability, firstly in terms of the frequency in the timetable, i.e., the number of • planned services. Secondly, in terms of the timetable due to delays, i.e., the number of actual services. The number of transfers. This inconvenience element is meant to be in addition to • the time spent waiting. Variability in the traveling time due to unforeseen reasons. • The amount and quality of information provided. • Crowding due to overloaded trains. • For a more detailed analysis of passenger convenience elements, see [WAC+14]. These two position papers summarize very extensively the two main contradicting goals of railways operations, namely, reducing operators’ costs and improving passengers’ con- venience. In this thesis different aspects of these contradicting views are analyzed in the presented publications. Mainly, passenger convenience goals are addressed without losing sight of the operators’ perspective. In [CHS14] (see Addendum A) an estimate for passengers’ traveling time is min- • imized and an acceptable distance to access the rail system for the passengers is ensured. Two integer programming formulations are proposed and, together with an additional integer program from literature, their performances are compared. In this work passengers’ traveling time as well as access and egress time are considered. Thus, this work mainly addresses passenger convenience. The summary of this work is given in Section 3.1. 2 In [GHS15a] (see Addendum B) line pools, composing sets of potential lines, are • generated with a focus on generalized costs and a simultaneous view on passenger transfers. An algorithm solving the arising model is proposed and various influential parameters are analyzed. This work can be classified to consider both operator costs and passenger convenience. It is summarized in Section 3.2. The objective of [Har15] (see Addendum C) is to find lines which minimize passenger • transfers. Thereby, it is intended to show that the resulting lines serve well in order to combat delays. In order to ensure that not too many lines are used, we bound the number of trains on each edge. The resulting model is formulated as an integer program and a heuristic algorithm is proposed to solve the program. This work mainly addresses passenger convenience in two aspects, which are passenger transfers and availability, but also regards the costs. The summary of this work can be found in Section 3.3. The work [HRS15] (see Addendum D) focuses on the utilization of railway infrastruc- • ture. It is motivated by the situation in India, in which trains are highly overloaded and using the infrastructure more efficiently is striven for. This work states a model for the optimal utilization of the infrastructure and is concerned with the complexity of the problem. The utilization of the infrastructure is, in the first place, one of the major cost aspects. However, also important elements of passengers’ convenience are addressed. Hence, this work emphasizes on both costs and passenger convenience perspectives. In Section 3.4 this work is summarized. In comparison