# Understanding Traffic Congestion via Network Analysis, Agent Modeling, and the Trajectory of Urban Expansion: A Coastal City Case

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Case of Study: Cartagena de Indias

^{2}and a population of approximately one million residents (1,028,736 in 2020) according to the last national census in 2018. It has an influx of tourists (nonresident foreigners) and visitors who totaled 530,177 (2019) people per year, before the outbreak of COVID-19. These visitors moved through an urban area (which, in 2019, was just under 82 km

^{2}of the 559 km

^{2}of the city’s total area) that comprises the historic city center and other relevant places [28]. Due to the diversity of economic activities in the city that includes industry, port logistics, commerce, and cultural promotion, the city is recognized as a well-known productive and economic hub of the country. The infrastructure of urban mobility has evolved towards a road network with a total length of 1359 km (Authors’ calculation based on GIS Data of Open Street Map (OSM)), with only 321 km (23.6% of the total) of these constituting main roads or avenues capable of supporting public transport vehicles of different dimensions. This road network was developed despite the physiography of the city of Cartagena, which is characterized by an extensive network of wetlands, canals, and lagoons, in addition to the 198 km of coastline and an important insular system (see Figure 1). Altogether, Cartagena’s urban mobility network is composed of a complex mix of convergent flows linked to import/export cargo, the supply and distribution of goods and merchandise, as well as the itineraries of residents and visitors from neighboring municipalities.

- Most daily trips are made to/from the historic city center, since it is the locus of many institutions and enterprises. Moreover, in the city, we find a convergence of touristic circuits coming from the airport, the harbor, and the bus terminal. The influx of vehicles comes via the Pedro de Heredia Avenue.
- Another important flux in the network is formed by industrial workers traveling to the Mamonal Industrial Zone. It should be noted that it is in this area that cargo operation logistics are concentrated and large vehicles (cargo trucks) are therefore mixed with regular vehicles.
- The third type of flux is composed of interurban vehicles transporting workers from nearby municipalities (see Figure 1) including insular and rural areas.

## 3. Mathematical Methods

#### 3.1. Network Analysis

#### 3.2. Dynamics of Traffic Flow

- Scenario #1: Both departure and destination nodes are assigned randomly.
- Scenario #2: Departure and destination nodes are defined following a preferential assignment rule, seeking to emulate realistic commuting patterns:
- (i)
- 80% of the R agents created at each step are assigned a destination node within the historic city center and the Mamonal Industrial Zone, the main centers of gravity as described in Section 2. The other 20% are assigned randomly across the nongravity nodes.
- (ii)
- Similarly, 80% of the R agents created at each step are assigned a departure node in the peripheral area, namely nodes from the northern, eastern, and southernmost areas. The remaining 20% of departure nodes are assigned randomly across the nonperipheral nodes.

## 4. Results

#### 4.1. Network Analysis

#### 4.2. Dynamics of Traffic Flow

## 5. Conclusions

#### 5.1. Summary and Discussion

#### 5.2. Limitations and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Evolution of the Urban Configuration of Cartagena

- The first and the oldest is the so-called historic center (see the orange region in Figure 2), established as a UNESCO World Heritage Site in 1988. It is the original outpost of the conquest and the colonial viceroyalty, between the XVI and XVIII centuries. It also served as the port of extraction of resources from New Granada, and the slave trade. This “old city” is segregated from the rest of the later urban expansion due to its walled defense architecture surrounded by the sea, lagoon bodies, and water pipes, which allowed its defense during the colony. Later, after the independence in the 19th century, the old city was linked to the interior of the country through a railroad. On this route, once the railway system was dismantled in 1930, the main road was built between 1969–1971, called Pedro de Heredia Avenue, until today the main and most congested road in the urban area [42].
- The second enclave is the Mamonal Industrial Complex born with the construction of the oil refinery in 1957 (light-violet region in Figure 2). The increasing number of facilities and docks (more than 36) evolved toward the consolidation of the “cargo corridor” absorbing some already consolidated urban routes to favor heavy cargo traffic that dangerously mixes with urban logistics.
- The third enclave is the touristic hotel area (yellow region in Figure 2), which, starting from the historic center, creates narrow strip of land with a peninsula. Since 1990, the tourism of the city grew toward the group of neighboring islands (Los Corales Natural Park) and more recently towards the north, following the coastal strip. It is appropriate to say that the aforementioned enclaves have occupied most of the coastal strip and low tide, and therefore access to the sea and inland water bodies.

## References

- Pumain, D.; Saint-Julien, T. Análisis Espacial: Las Interacciones; Universidad de Concepción-Facultad de Arquitectura, Urbanisme y Geografía: Concepción, Chile, 2014. [Google Scholar]
- Barthélemy, M. Spatial networks. Phys. Rep.
**2011**, 499, 1–101. [Google Scholar] [CrossRef] [Green Version] - Crucitti, P.; Latora, V.; Porta, S. Centrality measures in spatial networks of urban streets. Phys. Rev. E
**2006**, 73, 036125. [Google Scholar] [CrossRef] [Green Version] - Crucitti, P.; Latora, V.; Porta, S. Centrality in networks of urban streets. Chaos Interdiscip. J. Nonlinear Sci.
**2006**, 16, 015113. [Google Scholar] [CrossRef] [PubMed] - Duan, Y.; Lu, F. Robustness of city road networks at different granularities. Phys. A Stat. Mech. Appl.
**2014**, 411, 21–34. [Google Scholar] [CrossRef] - Manley, E.; Cheng, T. Understanding road congestion as an emergent property of traffic networks. In Proceedings of the 14th WMSCI, Orlando, FL, USA, 29 June–2 July 2010. [Google Scholar]
- Nagel, K.; Paczuski, M. Emergent traffic jams. Phys. Rev. E
**1995**, 51, 2909. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jayasinghe, A.; Sano, K.; Nishiuchi, H. Explaining traffic flow patterns using centrality measures. Int. J. Traffic Transp. Eng.
**2015**, 5, 134–149. [Google Scholar] [CrossRef] [Green Version] - Lämmer, S.; Gehlsen, B.; Helbing, D. Scaling laws in the spatial structure of urban road networks. Phys. A Stat. Mech. Appl.
**2006**, 363, 89–95. [Google Scholar] [CrossRef] [Green Version] - Gallelli, V.; Perri, G.; Vaiana, R. Operational and Safety Management at Intersections: Can the Turbo-Roundabout Be an Effective Alternative to Conventional Solutions? Sustainability
**2021**, 13, 5103. [Google Scholar] [CrossRef] - Macioszek, E. Roundabout Entry Capacity Calculation—A Case Study Based on Roundabouts in Tokyo, Japan, and Tokyo Surroundings. Sustainability
**2020**, 12, 1533. [Google Scholar] [CrossRef] [Green Version] - Davidović, S.; Bogdanović, V.; Garunović, N.; Papić, Z.; Pamučar, D. Research on Speeds at Roundabouts for the Needs of Sustainable Traffic Management. Sustainability
**2021**, 13, 399. [Google Scholar] [CrossRef] - Auttakorn, S. Assessment of traffic flow benefits of flyovers: A case study. J. Soc. Transp. Traffic Stud. (JSTS)
**2013**, 4, 1–9. [Google Scholar] - Headrick, J.; Uddin, W. Traffic flow microsimulation for performance evaluation of roundabouts and stop-controlled intersections at highway overpass. Adv. Transp. Stud.
**2014**, 34, 7–18. [Google Scholar] - Ran, B.; Boyce, D. Modeling Dynamic Transportation Networks: An Intelligent Transportation System Oriented Approach; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012. [Google Scholar]
- Nagatani, T. The physics of traffic jams. Rep. Prog. Phys.
**2002**, 65, 1331. [Google Scholar] [CrossRef] [Green Version] - Orosz, G.; Wilson, R.E.; Stépán, G. Traffic jams: Dynamics and control. Philos. Trans. R. Soc. A
**2010**, 368, 4455–4479. [Google Scholar] [CrossRef] [PubMed] [Green Version] - van Wageningen-Kessels, F.; Van Lint, H.; Vuik, K.; Hoogendoorn, S. Genealogy of traffic flow models. EURO J. Transp. Logist.
**2015**, 4, 445–473. [Google Scholar] [CrossRef] [Green Version] - Bazzan, A.L.; Klügl, F. A review on agent-based technology for traffic and transportation. Knowl. Eng. Rev.
**2014**, 29, 375. [Google Scholar] [CrossRef] - Krajzewicz, D.; Erdmann, J.; Behrisch, M.; Bieker, L. Recent development and applications of SUMO-Simulation of Urban MObility. Int. J. Adv. Syst. Meas.
**2012**, 5, 128–138. [Google Scholar] - Smith, L.; Beckman, R.; Baggerly, K. TRANSIMS: Transportation Analysis and Simulation System; Technical Report; Los Alamos National Lab.: Los Alamos, NM, USA, 1995. [Google Scholar]
- Horni, A.; Nagel, K.; Axhausen, K.W. The Multi-Agent Transport Simulation MATSim; Ubiquity Press: London, UK, 2016. [Google Scholar]
- Echenique, P.; Gómez-Gardenes, J.; Moreno, Y. Dynamics of jamming transitions in complex networks. EPL Europhys. Lett.
**2005**, 71, 325. [Google Scholar] [CrossRef] [Green Version] - Sreenivasan, S.; Cohen, R.; López, E.; Toroczkai, Z.; Stanley, H.E. Structural bottlenecks for communication in networks. Phys. Rev. E
**2007**, 75, 036105. [Google Scholar] [CrossRef] [Green Version] - De Martino, D.; Dall’Asta, L.; Bianconi, G.; Marsili, M. Congestion phenomena on complex networks. Phys. Rev. E
**2009**, 79, 015101. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Yan, G.; Zhou, T.; Hu, B.; Fu, Z.Q.; Wang, B.H. Efficient routing on complex networks. Phys. Rev. E
**2006**, 73, 046108. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Colak, S.; Schneider, C.M.; Wang, P.; González, M.C. On the role of spatial dynamics and topology on network flows. New J. Phys.
**2013**, 15, 113037. [Google Scholar] [CrossRef] [Green Version] - Amezquita-Lopez, J. Competitividad y Sostenibilidad de Cartagena de Indias; InterNaciones: Guadalajara, Mexico, 2017; Volume 6. [Google Scholar]
- Porta, S.; Crucitti, P.; Latora, V. The network analysis of urban streets: A primal approach. Environ. Plan. B Plan. Des.
**2006**, 33, 705–725. [Google Scholar] [CrossRef] [Green Version] - Xie, F.; Levinson, D. Measuring the structure of road networks. Geogr. Anal.
**2007**, 39, 336–356. [Google Scholar] [CrossRef] - Zhao, L.; Lai, Y.C.; Park, K.; Ye, N. Onset of traffic congestion in complex networks. Phys. Rev. E
**2005**, 71, 026125. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Universidad de Cartagena and Alcaldía Distrital de Cartagena. Diagnóstico del Distrito de Cartagena en materia de ordenamiento territorial. In Documento de Seguimiento y Evaluación de los Resultados Obtenidos Respecto de los Objetivos Planteados en el Plan de Ordenamiento Territorial Vigente del Distrito de Cartagena; Universidad de Cartagena: Cartagena, Colombia, 2010. [Google Scholar]
- Barthelemy, M.; Bordin, P.; Berestycki, H.; Gribaudi, M. Self-organization versus top-down planning in the evolution of a city. Sci. Rep.
**2013**, 3, 1–8. [Google Scholar] - Reynoso, C. Redes Sociales y Complejidad: Modelos Interdisciplinarios en la Gestión Sostenible de la Sociedad y la Cultura; Sb: Buenos Aires, Argentina, 2011. [Google Scholar]
- Gonzalez-Urango, H.; Inturri, G.; Le Pira, M.; García-Melón, M. Planning for Pedestrians with a participatory multicriteria approach. J. Urban Plan. Dev.
**2020**, 146, 05020007. [Google Scholar] [CrossRef] - Gómez-Lobo, A. Transit reforms in intermediate cities of Colombia: An ex-post evaluation. Transp. Res. Part A Policy Pract.
**2020**, 132, 349–364. [Google Scholar] [CrossRef] - Chen, S.; Huang, W.; Cattani, C.; Altieri, G. Traffic dynamics on complex networks: A survey. Math. Probl. Eng.
**2012**, 2012, 732698. [Google Scholar] [CrossRef] - Ben-Akiva, M.; Bierlaire, M. Discrete choice models with applications to departure time and route choice. In Handbook of Transportation Science; Springer: Berlin/Heidelberg, Germany, 2003; pp. 7–37. [Google Scholar]
- Wardman, M.; Chintakayala, V.P.K.; de Jong, G. Values of travel time in Europe: Review and meta-analysis. Transp. Res. Part A Policy Pract.
**2016**, 94, 93–111. [Google Scholar] [CrossRef] - Birolini, S.; Malighetti, P.; Redondi, R.; Deforza, P. Access mode choice to low-cost airports: Evaluation of new direct rail services at Milan-Bergamo airport. Transp. Policy
**2019**, 73, 113–124. [Google Scholar] [CrossRef] - López, J.A. La competitividad en el marco de políticas para ciudades sostenibles: Caso Cartagena, Colombia. InterNaciones
**2018**, 13, 101–130. [Google Scholar] - Ortiz, C.J. Un Diablo al que le Llaman Tren. El Ferrocarril Cartagena-Calamar; Fondo de Cultura Económica: Bogotá, Colombia, 2018. [Google Scholar]
- Mariaca, D.A.R.; Calán, C.A.G.; Molina, C.J. La accesibilidad terrestre a los puertos marítimos de Colombia. Una aproximación desde la equidad territorial. Entorno Geográfico
**2018**, 15, 8–47. [Google Scholar] [CrossRef]

**Figure 1.**Geographical location of Cartagena. The map was generated based on information from the following sources: Instituto Geográfico Agustin Codazzi (IGAC), Secretaria de Planeación del distrito de Cartagena, and World Topography map ESRI.

**Figure 3.**Schematic representation of the algorithm for a given agent. Agent’s current position ${n}_{0}$ is shown in the node with triangular shape and destination ${n}_{f}$ with rectangular shape. Two possible choices ${r}_{1}$ and ${r}_{2}$ toward the destination node are depicted in red with different intersections along the route (circles). The road length is shown next to each link and the occupation of the node q is shown with the number of points at the intersection.

**Figure 4.**Distributions in Cartagena’s road network. (

**A**) Streets’ length: Main figure shows the distribution in linear scale truncated to roads smaller than 1 km. Inset: Same as main figure in log-lin scale, revealing an exponential decay of the distribution. (

**B**) Distribution of distances in Cartagena’s road map (blue) and the characteristic path length (red). Inset: Same as in main figure in log-lin scale showing the exponential decay of the distance distribution. (

**C**) Angles between intersections.

**Figure 5.**Spatial distribution of centrality measures in Cartagena’s street network: (

**A**) Closeness centrality and (

**B**) Betweenness centrality. The values in the color map correspond to the z-score of each indicator.

**Figure 6.**Cumulative distributions of centrality measures. CDF for (

**A**) closeness centrality and (

**B**) betweenness centrality.

**Figure 7.**Different congestion cases with varying agent’s behavior under scenario #1.

**Left**panels: Distribution of arrival time.

**Middle**panel: Histogram of the occupation in the network.

**Right**panels: Spatial occupation of the network. In this figure, the panel (

**A**) refers to $h=0.5$, panel (

**B**) $h=0.9$, and panel (

**C**) $h=1$. For this simulation, $R=5$ was fixed and the system was simulated through 1500 iterations, discarding the first 500 iterations, which were considered as transient behavior.

**Figure 8.**Different congestion cases with varying agent’s behavior under scenario #2.

**Left**panels: Distribution of arrival time.

**Middle**panel: Histogram of the occupation in the network.

**Right**panels: Spatial occupation of the network. In this figure, the panel (

**A**) refers to $h=0.5$, panel (

**B**) $h=0.9$, and panel (

**C**) $h=1$. For this simulation, $R=5$ was fixed and the system was simulated through 1500 iterations discarding the first 500 iterations considered transient behavior.

**Figure 9.**Average statistics as a function of h: (

**A**) Arrival time. (

**B**) Occupation larger than 0. (

**C**) Fraction of nonarrived agents (

**D**) Order parameter. In all panels, insets refer to the corresponding indicator under scenario #2 averaged across 15 realizations. Error bars denote one standard deviation.

**Figure 10.**Correlation between occupation and (

**A**) closeness centrality and (

**B**) betweenness centrality at each node for scenario #1. In both panels, insets refer to the corresponding indicator under scenario #2 with $R=5$, averaged across 15 realizations. Error bars denote one standard deviation.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Amézquita-López, J.; Valdés-Atencio, J.; Angulo-García, D.
Understanding Traffic Congestion via Network Analysis, Agent Modeling, and the Trajectory of Urban Expansion: A Coastal City Case. *Infrastructures* **2021**, *6*, 85.
https://doi.org/10.3390/infrastructures6060085

**AMA Style**

Amézquita-López J, Valdés-Atencio J, Angulo-García D.
Understanding Traffic Congestion via Network Analysis, Agent Modeling, and the Trajectory of Urban Expansion: A Coastal City Case. *Infrastructures*. 2021; 6(6):85.
https://doi.org/10.3390/infrastructures6060085

**Chicago/Turabian Style**

Amézquita-López, Julio, Jorge Valdés-Atencio, and David Angulo-García.
2021. "Understanding Traffic Congestion via Network Analysis, Agent Modeling, and the Trajectory of Urban Expansion: A Coastal City Case" *Infrastructures* 6, no. 6: 85.
https://doi.org/10.3390/infrastructures6060085