The Railway Line Frequency and Size Setting Problem

[EN] The problem studied in this paper takes as input data a set of lines forming a railway network, and an origin¿destination (OD) matrix. The OD pairs may use either the railway network or an alternative transportation mode. The objective is to determine the frequency/headway of each line as well as its number of carriages, so that the net profit of the railway network is maximized. We propose a mixed integer non-linear programming formulation for this problem. Because of the computational intractability of this model, we develop four algorithms: a mixed integer linear programming (MIP) model, a MIP-based iterative algorithm, a shortest-path based algorithm, and a local search. These four algorithms are tested and compared over a set of randomly generated instances. An application over a case study shows that only the local search heuristic is capable of dealing with large instances.This research was partly funded by the Canadian Natural Sciences and Engineering Research Council under Grant 2015-06189, by the Ministerio de Economía y Competitividad (Spain)/FEDER under projects MTM2012-37048, MTM2015-67706-P and DPI2012-36243-C02-01, and by Junta de Andalucía (Spain)/FEDER under excellence project P10-FQM-5849. Part of this research was done while Federico Perea was enjoying a research visit to CIRRELT, funded by the Universitat Politècnica de València, under program PAID-00-15. This support is gratefully acknowledged. Thanks are due to the referees for their valuable comments.De-Los-Santos, A.; Laporte, G.; Mesa, JA.; Perea Rojas Marcos, F. (2017). The Railway Line Frequency and Size Setting Problem. Public Transport. 9(1-2):33-53. https://doi.org/10.1007/s12469-017-0154-2S335391-2Albrecht T (2009) Automated timetable design for demand-oriented service on suburban railways. Public Transport 1(1):5–20Caprara A, Kroon L, Monaci M, Peeters M, Toth P (2007) Passenger Railway optimization. In: Barnhart C, Laporte G (eds) Handbooks in operations research and management science, vol 14. Transportation, chapter 3. North-Holland, Amsterdam, pp 129–187De-Los-Santos A, Laporte G, Mesa J, Perea F (2014) Simultaneous frequency and capacity setting in uncapacitated metro lines in presence of a competing mode. Transp Res Proc 3:289–298Desaulniers G, Hickman M (2007) Public transport. In: Barnhart C, Laporte G (eds) Handbook in operations research and management science, vol 14, Transportation, chapter 2. North-Holland, Amsterdam, pp 69–127Gallo M, Montella B, D’Acierno L (2011) The transit network design problem with elastic demand and internalisation of external costs: An application to rail frequency optimisation. Transp Res Part C Emerg Technol 19(6):1276–1305Laporte G, Marín A, Mesa JA, Perea F (2011) Designing robust rapid transit networks with alternative routes. J Adv Transp 45(1):54–65Marín A, García-Ródenas R (2009) Location of infrastructure in urban railway networks. Comput Oper Res 36(5):1461–1477Michaelis M, Schöbel A (2009) Integrating line planning, timetable, and vehicle scheduling: a customer oriented heuristic. Public Transport 1(3):211–232Perea F, Mesa JA, Laporte G (2014) Adding a new station and a road link to a road-rail network in the presence of modal competition. Transp Res Part B Methodol 68:1–16Schmidt M, Schöbel A (2015) The complexity of integrating passenger routing decisions in public transportation models. Networks 65(3):228–243Schmidt ME (2014) Integrating routing decisions in public transportation problems. Springer, New YorkSchöbel A (2012) Line planning in public transportation. OR Spectrum 34:491–510van Oort N, van Nes R (2009) Regularity analysis for optimizing urban transit network design. Public Transport 1(2):155–168Vuchic VR (2005) Urban transit: operations, planning, and economics. Wiley, Hoboken, New Jerse

Network Centrality of Metro Systems

Whilst being hailed as the remedy to the world’s ills, cities will need to adapt in the 21st century. In particular, the role of public transport is likely to increase significantly, and new methods and technics to better plan transit systems are in dire need. This paper examines one fundamental aspect of transit: network centrality. By applying the notion of betweenness centrality to 28 worldwide metro systems, the main goal of this paper is to study the emergence of global trends in the evolution of centrality with network size and examine several individual systems in more detail. Betweenness was notably found to consistently become more evenly distributed with size (i.e. no “winner takes all”) unlike other complex network properties. Two distinct regimes were also observed that are representative of their structure. Moreover, the share of betweenness was found to decrease in a power law with size (with exponent 1 for the average node), but the share of most central nodes decreases much slower than least central nodes (0.87 vs. 2.48). Finally the betweenness of individual stations in several systems were examined, which can be useful to locate stations where passengers can be redistributed to relieve pressure from overcrowded stations. Overall, this study offers significant insights that can help planners in their task to design the systems of tomorrow, and similar undertakings can easily be imagined to other urban infrastructure systems (e.g., electricity grid, water/wastewater system, etc.) to develop more sustainable cities