Complex networks for the analysis and simulation of intermunicipal public transportation: A case study of the Department of Quindío, Colombia

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Abstract

This paper presents an integrated methodological framework for analyzing the structure and operational performance of intercity public transportation systems by combining complex network theory with discrete event simulation. The road network is modeled as a directed multigraph, enabling the identification of critical nodes and corridors through centrality metrics and percolation analysis, while the simulation operates directly on the network’s topology by incorporating travel speed variability, passengers’ boarding and alighting times, and service frequencies. A case study of the intercity public transportation network of the Department of Quindío (Colombia) demonstrates the applicability of the methodology. The results show that network vulnerability is concentrated in a limited number of strategic corridors, with betweenness centrality providing the most effective criterion for identifying structurally critical nodes. Furthermore, although alternative routes exist, they do not necessarily guarantee operational resilience. The proposed framework provides a quantitative decision support tool for transportation planning and infrastructure management and, owing to its modular and scalable design, can be readily adapted to other intercity transportation systems.

Keywords

complex networks / directed multigraph / public transportation / discrete event simulation / queueing theory / network resilience / intercity mobility

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References

[1] INRIX Research, 2024 Global Traffic Scorecard ,Technical report,INRIX,Inc.,Kirkland,WA,2024(Accessed:January 2025).Available from:https://inrix.com/scorecard/.

[2] TomTom Traffic Index, TomTom Traffic Index 2023: Global Traffic Congestion Rankings ,Technical report,TomTom International BV,2024(Accessed:January 2024).Available from:https://www.tomtom.com/.

[3] BRT Data,Global BRT Data-Ridership Statistics,Online database,2023(Accessed:September 2024).Available from:https://brtdata.org/.

[4] EMBARQ,On the Move:The Global Rise of Mass Transit,Smart Cities Dive,2014.Available from:https://www.smartcitiesdive.com/ex/sustainablecitiescollective/move-global-rise-mass-transit/200656/.

[5] UITP-International Association of Public Transport, Global Economic Outlook 2024: Public Transport Trends and Statistics ,Technical report,UITP,Brussels,Belgium,2024(Accessed:September 2024).Available from:https://www.uitp.org/publications/global-economic-outlook-2024/.

[6] D.C.Mestra Sierra,M.A.Rodriguez Peniche,D.M.Rodriguez Herrera,T.O.Boyano Fram,Land transport mobility in the urban-rural context of Colombia,Saber Cienc.Libertad Germ., 17(2024),162-168.https://doi.org/10.18041/2382-3755/germinacion.2024v17.12233

[7] L.A.Guzman,S.G.Cardona,J.L.Ochoa,Increased ridership and improved affordability:Transforming public transport subsidies in developing contexts,Res.Transp.Econ., 108(2024),101492.https://doi.org/10.1016/j.retrec.2024.101492

[8] M.Islam,G.Kabir,M.R.Anis,Evaluating enso-driven risks to strengthen transportation system resilience of canadian provinces,Can.J.Civ.Eng., 52(2025),1630-1644.https://doi.org/10.1139/cjce-2025-0118

[9] H.A.Moreno,M.C.Vélez Ortiz,J.D.Montoya,R.Rhenals Monterrosa,Rainfall and landslides in Antioquia:Analysis of their occurrence at interannual,intra-annual,and daily scales,Rev.EIA, 5(2006),59-69.Available from:https://dialnet.unirioja.es/servlet/articulo?codigo=5557900.

[10] O.Bello,L.Ortiz,J.Samaniego, Estimation of the Effects of Disasters in Latin America, 1972-2010 ,CEPAL,Medio Ambiente y Desarrollo Series No.157,LC/L.3899,United Nations,Santiago,Chile,2014(Accessed:January 2025).Available from:https://repositorio.cepal.org/server/api/core/bitstreams/f10005fd-faf1-4fe4-8edf-40d0cc33fd16/content.

[11] S.Boccaletti,V.Latora,Y.Moreno,M.Chavez,D.U.Hwang,Complex networks:Structure and dynamics,Phys.Rep., 424(2006),175-308.https://doi.org/10.1016/j.physrep.2005.10.009

[12] E.Estrada, The Structure of Complex Networks:Theory and Applications ,Oxford University Press,2011.https://doi.org/10.1093/acprof:oso/9780199591756.001.0001

[13] M.Newman, Networks ,Oxford University Press,2018.https://doi.org/10.1093/oso/9780198805090.001.0001

[14] Z.Xu,S.S.Chopra,H.Lee,Resilient urban public transportation infrastructure:A comparison of five flow-weighted metro networks in terms of the resilience cycle framework,IEEE Trans.Intell.Transp.Syst., 23(2022),12688-12699.https://doi.org/10.1109/tits.2021.3116667

[15] C.Chen,S.Wang,J.Zhang,X.Gu,Modeling the vulnerability and resilience of interdependent transportation networks under multiple disruptions,J.Infrastruct.Syst., 29(2023),04022043.https://doi.org/10.1061/jitse4.iseng-2185

[16] J.Tang,L.Xu,C.Luo,T.S.A.Ng,Multi-disruption resilience assessment of rail transit systems with optimized commuter flows,Reliab.Eng.Syst.Saf., 214(2021),107715.https://doi.org/10.1016/j.ress.2021.107715

[17] N.Yadav,S.Chatterjee,A.R.Ganguly, Resilience of urban transport network-of-networks under intense flood hazards exacerbated by targeted attacks,Sci.Rep., 10(2020),10350.https://doi.org/10.1038/s41598-020-66049-y

[18] R.W.Hall,Transportation queueing,inHandbook of Transportation Science ,2003,113-153.https://doi.org/10.1007/0-306-48058-1 5

[19] N.Gautam, Analysis of Queues: Methods and Applications ,CRC Press,2012.https://doi.org/10.1201/b11858

[20] B.X.Dong,M.Shan,B.G.Hwang,Simulation of transportation infrastructures resilience:A comprehensive review,Environ.Sci.Pollut.Res., 29(2022),12965-12983.https://doi.org/10.1007/s11356-021-18033-w

[21] M.Neagoe,H.H.Hvolby,M.S.Taskhiri,P.Turner,Using discrete-event simulation to compare congestion management initiatives at a port terminal,Simul.Model.Pract.Theory, 112(2021),102362.https://doi.org/10.1016/j.simpat.2021.102362

[22] Z.Lyu,D.Pons,Y.Zhang,Z.Ji,Freight operations modelling for urban delivery and pickup with flexible routing:Cluster transport modelling incorporating discrete-event simulation and GIS,Infrastructures, 6(2021),180.https://doi.org/10.3390/infrastructures6120180

[23] O.A.Sediek,S.El-Tawil,J.McCormick,Modeling interdependencies between the building portfolio,transportation network,and healthcare system in community resilience,Nat.HazardsRev., 23(2022),04021060.https://doi.org/10.1061/(asce)nh.1527-6996.0000538

[24] S.Dudin,A.Dudin,R.Manzo,L.RaritàAnalysis of semi-open queueing network with correlated arrival process and multi-server nodes,Oper.Res.Forum, 5(2024),99.https://doi.org/10.1007/s43069-024-00383-z

[25] A.Dudin,S.Dudin,R.Manzo,L.RaritàQueueing system with batch arrival of heterogeneous orders,flexible limited processor sharing and dynamical change of priorities,AIMS Math., 9(2024),12144-12169.https://doi.org/10.3934/math.2024593

[26] A.Dudin,S.Dudin,R.Manzo,L.RaritàAnalysis of multi-server priority queueing system with hysteresis strategy of server reservation and retrials,Mathematics, 10(2022),3747.https://doi.org/10.3390/math10203747

[27] G.Boeing,OSMnx:New methods for acquiring,constructing,analyzing,and visualizing complex street networks,Comput.Environ.Urban Syst., 65(2017),126-139.https://doi.org/10.1016/j.compenvurbsys.2017.05.004

[28] G.Boeing,Urban street network analysis in a computational notebook,REGION , 6(2020),39-51.https://doi.org/10.18335/region.v6i3.278

[29] P.Crucitti,V.Latora,S.Porta,Centrality measures in spatial networks of urban streets,Phys.Rev.E, 73(2006),036125.https://doi.org/10.1103/physreve.73.036125

[30] W.Liu,X.Li,T.Liu,B.Liu,Approximating betweenness centrality to identify key nodes in a weighted urban complex transportation network,J.Adv.Transp.,2019(2019),9024745.https://doi.org/10.1155/2019/9024745

[31] Departamento Administrativo Nacional de Estadística(DANE),Censo Nacional de Población y Vivienda(CNPV)2018:Presentación Quindío-Armenia,2019(Accessed:January 30,2026).Available from:https://www.dane.gov.co/files/censo2018/informacion-tecnica/presentaciones-territorio/190731-CNPV-presentacion-Quindio-Armenia.pdf.

[32] OpenStreetMap contributors,OpenStreetMap,2024(Accessed:January 30,2026).Available from:https://www.openstreetmap.org/.

[33] R.Diestel, Graph Theory ,5th(ed),Springer,Berlin,2017.https://doi.org/10.1007/978-3-662-53622-3

[34] S.H.Strogatz,Exploring complex networks,Nature, 410(2001),268-276.https://doi.org/10.1038/35065725

[35] L.Fraccascia,I.Giannoccaro,V.Albino,Resilience of complex systems:State of the art and directions for future research,Complexity,2018(2018),3421529.https://doi.org/10.1155/2018/3421529

[36] L.D.F.Costa,Reinforcing the resilience of complex networks,Phys.Rev.E, 69(2004),066127.https://doi.org/10.1103/physreve.69.066127

[37] G.Paul,S.Sreenivasan,H.E.Stanley,Resilience of complex networks to random breakdown,Phys.Rev.E, 72(2005),056130.https://doi.org/10.1103/physreve.72.056130

[38] J.Gao,B.Barzel,A.L.Barabási,Universal resilience patterns in complex networks,Nature, 530(2016),307-312.https://doi.org/10.1038/nature16948

[39] SimPy Community,SimPy Documentation(Accessed:January 7,2026).Available from:https://simpy.readthedocs.io/.

[40] J.Zhang,Y.Luo,Degree centrality,betweenness centrality,and closeness centrality in social network,in2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017) ,Bankog,Thailand,2017,300-303.https://doi.org/10.2991/msam-17.2017.68

[41] E.Cohen,D.Delling,T.Pajor,R.F.Werneck,Computing classic closeness centrality,at scale,inCOSN ’14:Proceedings of the second ACM conference on Online social networks ,New York,NY,USA,2014,37-50.https://doi.org/10.1145/2660460.2660465

[42] A.Cuzzocrea,A.Papadimitriou,D.Katsaros,Y.Manolopoulos,Edge betweenness centrality:A novel algorithm for QoS-based topology control over wireless sensor networks,J.Netw.Comput.Appl., 35(2012),1210-1217.https://doi.org/10.1016/j.jnca.2011.06.001

[43] A.Kazerani,S.Winter,Can betweenness centrality explain traffic flow,inProceedings of the 12thAGILE International Conference,Springer,2009.

[44] M.Newman, Networks: An Introduction ,Oxford University Press,2010.https://doi.org/10.1093/acprof:oso/9780199206650.001.0001

[45] M.Krnc,J.S.Sereni,R.Škrekovski,Z.B.Yilma,Eccentricity of networks with structural constraints,Discuss.Math.GraphTheory, 40(2020),1141-1162.https://doi.org/10.7151/dmgt.2180

[46] Y.Zhang, New Frontiers in Graph Theory ,Intech,2012.https://doi.org/10.5772/1965

[47] P.Bonacich,Some unique properties of eigenvector centrality,Soc.Networks, 29(2007),555-564.https://doi.org/10.1016/j.socnet.2007.04.002

[48] B.Ruhnau,Eigenvector-centrality-A node-centrality? Soc.Networks, 22(2000),357-365.https://doi.org/10.1016/s0378-8733(00)00031-9

[49] L.SoláM.Romance,R.Criado,J.Flores,A.García del Amo,S.Boccaletti,Eigenvector centrality of nodes in multiplex networks,Chaos, 23(2013),033131.https://doi.org/10.1063/1.4818544

[50] S.Porta,P.Crucitti,V.Latora,The network analysis of urban streets:A dual approach,PhysicaA, 369(2006),853-866.https://doi.org/10.1016/j.physa.2005.12.063

[51] P.Crucitti,V.Latora,S.Porta,Centrality in networks of urban streets,Chaos , 16(2006),015113.https://doi.org/10.1063/1.2150162

[52] E.López,R.Parshani,R.Cohen,S.Carmi,S.Havlin,Limited path percolation in complex networks,Phys.Rev.Lett., 99(2007),188701.https://doi.org/10.1103/physrevlett.99.188701

[53] M.A.Serrano,M.Bogu˜náClustering in complex networks.II.Percolation properties,Phys.Rev.E, 74(2006),056115.https://doi.org/10.1103/physreve.74.056115

[54] R.Cohen,S.Havlin, Percolation in Complex Networks ,Springer,New York,NY,2021,419-431.https://doi.org/10.1007/978-1-0716-1457-0 383

[55] A.Allard,L.Hébert-Dufresne,Percolation and the effective structure of complex networks,Phys.Rev.X, 9(2019),011023.https://doi.org/10.1103/physrevx.9.011023

[56] Y.Y.Liu,E.Csóka,H.Zhou,M.Pósfai,Core percolation on complex networks,Phys.Rev.Lett., 109(2012),205703.https://doi.org/10.1103/physrevlett.109.205703

[57] M.Li,R.R.Liu,L.LüM.B.Hu,S.Xu,Y.C.Zhang,Percolation on complex networks:Theory and application,Phys.Rep., 907(2021),1-68.https://doi.org/10.1016/j.physrep.2020.12.003