View source for Transportation Deployment Casebook/2025/Madrid Metro

== '''Introduction''' ==
The [[w:Madrid Metro|Madrid Metro]]is a rapid transit system serving the capital of Spain with 276 stations across its network. At a length of 293 km, it is the 14th longest rapid transit system in the world today. Operations began in 1919 with only one line that ran for 3.48 km and had 8 stations. Since the inauguration of the Madrid Metro, the system has expanded to accommodate the growing population. It now comprises 13 lines, with annual ridership exceeding 662 million passengers .


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== '''Qualitative Analysis''' ==
=== Mode Description ===
Rapid transit systems are high-capacity modes of public transport that operate on exclusive right-of-way steel tracks, powered electrically and free from other vehicles or pedestrian obstructions <ref name="source5">{{cite web |author=C. Parrott-Sheffer |title=Rapid transit |url=https://www.britannica.com/technology/rapid-transit |website=Encyclopædia Britannica |date=2025-03-07 |accessdate=2025-03-10}}</ref>. Primarily underground, metros have been developed over time in denser urban areas. The expansion of large metro networks across the world has resulted in exponential growth in passenger demand and the number of passengers using this mode of transport due to its efficiency <ref name="source6">{{cite journal |author=D. Lin, Z. Zhou, M. Weng, W. Broere, J. Cui |title=Metro systems: Construction, operation and impacts |journal=Tunnelling and Underground Space Technology |volume=143 |pages=105373 |year=2024 |url=https://doi.org/10.1016/j.tust.2023.105373}}</ref>. Metro transport has the ability to fulfil the mobility needs of a population in a metropolitan area if successful, enhancing accessibility between homes, schools, workplaces, and other leisure destinations, thus benefiting social, economic, and health outcomes <ref name="source6"/>.<br />

[[File:Madrid Metro Map.svg|'''Figure 1:''' Madrid Metro Map|thumb]]
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Before the Madrid Metro, London was the first city to construct an underground railway for the transportation of goods and passengers. The opening of the first line in 1863, spanning just over 6 km underground, revolutionised urban travel <ref name="source7">{{cite web |author=Á. Ibáñez |title=The History of the Metro: 160 Years of People Getting Around Under Cities Worldwide |url=https://blog.ferrovial.com/en/2022/04/history-of-metro-160-years-people-getting-around-under-cities/ |website=Ferrovial |date=2022-04-25 |accessdate=2025-03-08}}</ref>.<br />

Following the pioneering development of the London Underground, various cities soon followed. The Budapest Metro (Hungary) became the first in continental Europe, beginning operations in 1896, followed by the Paris Metro (France) in 1900 and Berlin’s U-Bahn (Germany) in 1902. In the United States, the New York subway system opened in 1904, followed by Philadelphia’s in 1907. Meanwhile, South America's first subway system was introduced in Buenos Aires (Argentina) in 1913. <ref name="source7"/>.<br />

Before the Madrid Metro's inauguration in 1919, the Spanish capital had over 50 tram lines, the first of which opened in May 1871. However, the tram system expanded unevenly and chaotically, as various different private companies requested and obtained licenses to develop their own networks. Historian Diego Gutiérrez describes this chaos stating, “The history of trams in Madrid … is the effort to link the city center with the periphery in all directions … different promoters with their own project” <ref name="source8">{{cite web |author=M. Á. Medina |title=Remembering Madrid’s golden age of trams |url=https://english.elpais.com/elpais/2018/03/21/inenglish/1521635250_710261.html |website=EL PAÍS English |date=2018-03-27 |accessdate=2025-03-08}}</ref>.

Before the introduction of electric power, Madrid’s trams were operated using donkey-drawn carriages and steam engines, which were inefficient, not as hygienic and noisy when compared to modes post electrification. The arrival of electricity in 1898 resulted in new problems surfacing with the new technology and innovation. The increased speed of electric trams led to a rise in accidents, some of which were fatal and even resulted in riots. Despite these challenges, the tram system continued to expand in Madrid, growing from 25 lines from 1905 to 50 in 1923.<br />

The Spanish Civil War caused extensive destruction to both the city and its tram network, leaving many trams severely damaged. While some routes were repaired, the entire network could not be fully restored, and trams were gradually replaced by buses. The last tram lines ceased operation in 1972, exactly 101 years after its launch. Many members of the public believed that trams caused traffic delays. By transitioning to an underground transit systems, delays were reduced, and public perception of urban transport improved.<br />

[[File:Madrid Trams.png|thumb|An image of an old tram in Madrid from the Historical Metropolitan Society of Madrid]]

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The invention and development of the London Underground required a combination of expertise from various engineering disciplines. Civil engineers played a major role in tunnel construction, using the cut-and-cover method to create underground passages through densely populated areas. Mechanical engineering contributed to development in the design of steam-powered locomotives that are able to function in enclosed environments, adapting existing railway technology of steam to the environment around underground travel. As the limitations of steam-powered trains became evident in poor air quality in tunnels and inefficient use of energy, the London Underground transitioned to electric traction. This shift required knowledge and innovation in electrical engineering, including the construction of power stations, integration of an electrified third rail or overhead power lines to replace steam. <br />

Modifications were also made to track gauge, rolling stock, and power sources. Narrow-gauge tracks were maintained for Madrid’s Metro historical lines and remains so through lines 1 to 5. However, for newer lines, international guidelines and standards of wider gauge (1445 mm) were catered to for ease of upgrading rolling stock and for development into areas with mountainous terrain. Methods of optimising space efficiency while allowing for future technological advancements is highly valued. Rolling stock designs have been enhanced with lightweight materials, streamlined aerodynamics, and energy-efficient systems as Madrid continues expanding its fleet to meet modern public transport demands. As of 2024, modernisation efforts include comprehensive programs aimed to extend the operational life cycle of new trains for the historical Line 1 while maintaining the narrow track gauge <ref name="source12">{{cite web |title=CAF also wins the contract to supply the second batch of trains for the Madrid metro |url=https://www.cafmobility.com/en/press-room/caf-wins-contract-supply-second-batch-trains-madrid-metro/ |website=Cafmobility.com |date=2024 |accessdate=2025-03-10}}</ref>. The system prioritises energy efficiency, in alignment with the city’s environmental policies, as well as safety and passenger comfort. This transition from steam to electric metro networks exemplifies the continuous evolution of urban transport technologies to meet growing urban mobility demands.

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=== Context and Birth of Madrid's Metro System ===
'''Early Market Development'''<br />
The early market niche was workers commuting and general urban mobility, as it reduced travel times compared to the trams at street level, which often experienced delays. After the inauguration in 1919, Line 1 was expanded, and Line 2 was constructed in response to the success of the original Line 1. By 1936, the network had three lines, all of which served as air raid shelters during the Spanish Civil War.<br />
After the Civil War, the community recovered slowly, which reduced the rate at which the metro developed. In 1944, a fourth line was constructed, incorporating part of Line 2, which had always been intended for Line 4. This demonstrates the developers' ability to plan ahead, reducing material and overall costs. During the 1960s and 1970s, the metro expanded to accommodate urban sprawl. To improve efficiency, larger platforms were introduced, but the narrow-bodied rolling stock to accommodate the track gauge was not significantly altered on the historical lines. A fifth metro line was constructed with narrow sections but 90-meter platforms, and Line 1 soon followed with an expansion of its platforms from 60 meters to 90 meters. With Madrid’s economic boom in the 1970s, the rapid growth in population led to large expansions, with new lines designed with larger 115-meter-long platforms.

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'''Birthing Phase and Early Policies'''<br />
Madrid Metro’s foundational design was inspired by the London Underground and Paris Metro systems, focusing on underground right-of-way transportation to ease congestion on street level. The government and policies developed played major roles in financing and planning throughout the birth and growth of Madrid’s Metro. This included fast-tracked approvals, prioritisation of cost-efficient construction, environmentally friendly and sustainable means, which shaped the city’s long-term trajectory in terms of technologies and rate of growth.<br />

Madrid was able to build at a low cost and efficient pace due to these policies, not without financial challenges of course. <ref name="source9">{{cite web |author=B. Hopkinson |title=How Madrid built its metro cheaply - Works in Progress |url=https://worksinprogress.co/issue/how-madrid-built-its-metro-cheaply/ |website=Worksinprogress.co |date=2024 |accessdate=2025-03-09}}</ref>
Fast, inexpensive deliveries were awarded by city-level powers, while the Community of Madrid concentrated planning, funding, and construction powers at the appropriate level to deliver the project. This enabled political leaders to make electoral promises about infrastructure, as their popularity and personal success would often be linked to the success of the project.<br />

Furthermore, the regional government streamlined environmental and planning processes, expediting construction by tunnelling 24/7. Trade-offs were carefully analysed, compared and considered between existing stations and lines, their design and costs, the complexity of signalling systems, and the testing required to determine the most effective system<ref name="source9"/>.<br />

Madrid also developed the state capacity needed to deliver projects, with experienced engineers and managers working in-house for both design and construction. The public company then had the flexibility to place funds in hiring experts and procurement of materials based on cost and quality, rather than solely minimising costs. <ref name="source9"/>.<br />

Unlike other cities, where infrastructure of stations became increasingly elaborate and costly over time, Madrid maintained its focus on functional, user-oriented designs. While metro expansions in other cities are often delayed due to extensive environmental reviews, Madrid’s streamlined environmental and bureaucratic approval process allowed for quick environmental assessments during expansion processes. This reduced the time required for approvals, allowing projects to move forward much faster and at lower costs. Government-imposed policies included the allocation of public funds to metro expansions, along with fare regulations and subsidies to ensure affordability, with the regional government playing a role in approval of expansion plans.<br />

'''Growth and Maturation of the Madrid Metro System'''<br />
The metro system was developed alongside broader sustainable mobility policies aimed to reduce congestion and enhance public transport efficiency. Madrid’s reliance on standardised station designs, consistent train models and contractors, and unified signalling systems ensured cost efficiency but also "locked in" certain design choices such as track gauge. This limited the flexibility to adopt newer and more experimental technologies in later expansions. <br />

The Madrid Metro undergoes constant changes and updates to accommodate new needs, new technologies and is an ever changing system. For example, Line 6 undergoing modernisation to accommodate automated driving in the future, where new rolling stock has to be accommodated for where it prioritises energy efficiency, with reductions in energy consumption compared to current models. These upgrades to the system are supported by financing from the European Investment Bank. However, there are still constraints due to “Lock-In” effects such as constraints from legacy infrastructure and historical planning decisions. The older historic stations and tunnels size limit the extent to which the system can be modernised, particularly regarding train sizes and platform designs due to track gauge and width of original trains. Furthermore, established policies and long-term contracts with suppliers like CAF (Construcciones y Auxiliar de Ferrocarriles) shape procurement decisions and potentially change the way in which the Madrid Metro grows, when constrained by previous decisions. Opportunities in gradual transition to fully automated lines to enhance efficiency, or integration with regional high-speed rail and regional transit will continue to expand the system to serve the future of Madrid metropolitan and regional areas for higher connectivity.

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== '''Quantitative Analysis''' ==
=== 1919 - 2024: Lifecycle ===
Data from Metro de Madrid's 2021 Corporate report <ref name="source2">{{cite web |title=Metro de Madrid Corporate Report 2021 |url=https://www.metromadrid.es/sites/default/files/documentos/Corporate_Report_2021_0.pdf |website=Metromadrid.es |date=2021 |accessdate=2025-03-08}}</ref> and Andersen, R. et al., (2022) <ref name="source1">{{cite journal |author=P. Xuto, R. Anderson, D. Graham, D. Hörcher |title=Sustainable urban rail funding: Insights from a century-long global dataset |year=2022 |url=https://doi.org/10.1016/j.tranpol.2022.10.005}}</ref> paper was used to analyse trends in annual ridership of Madrid's Metro from 1919 to 2024. 

Three clear phases can be identified: Most growth occurring post birth of the system (1919 - 1973), a general decline (1973-1987), a second growth / recovery with the effects of COVID-19 later on (1987 - present). Ridership data, specifically the number of passenger journeys is explored in this study. A three parameter logistic model is used to develop an S-curve that illustrates trends and changes during the birth, growth, maturity and saturation of the rapid transit system in Madrid. Seeking a curve that best fits the data, we assume the data takes a logistic shape. The following equation was used :<br />
<math>S(t) = K/[1+e^{(-b(t-t_0)}]</math><br />
Where:<br />
S(t) is the predicted system size at year t<br />
t is time (year)<br />
t_0 is the inflection point, midpoint<br />
K is saturation status levels<br />
b is a coefficient<br />
K and b are to be estimated<br />

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The life cycle model is represented by the following equation, demonstrating how ridership levels changed and evolved through the birth, growth and saturation/mature, of the transit model.:<br /> 
<math>Y = \ln\left(\cfrac{Passengers(t)}{(K-Passengers(t))}\right)= bt-bt_0</math>

[[File:Passenger Journeys Full Lifetime.png|thumb|'''Figure :'''Madrid de Metro: Number of Passenger Journeys 1919 - 2024]]<br />

'''Regression Results'''
{| table style="text-align:center;"  class="wikitable" border="1" cellpadding="4" cellspacing="0" style="border:\#c9c9c9 1px solid; margin: 1em 1em 1em 0; border-collapse: collapse;"
| align="center" style="background:#f0f0f0;"|'''Variable'''
| align="center" style="background:#f0f0f0;"|'''Value'''
|-
| K(S_Max)|| 740 
|-
| b|| 0.0396
|-
| t_i (tnought)|| 1971.7056
|-
| Intercept||-78.0895
|-
| R^2|| 0.7263
|}

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=== 1919 - 1973: Birth and Initial Growth ===
From its inauguration and opening in 1919 to 1973, Metro de Madrid’s birth and expansion forms a S-curve, typically used to describe life cycles of technology from birth to maturation. From 1919 to 1936, the birth and growth of the metro was steady, however, the trajectory changes from 1936, where Francisco Franco’s dictatorship would have had an influence on the growth rate of the metro. During the Spanish Civil War (1936-1939) <ref name="SpanishCivilWar">{{cite web |title=Spanish Civil War |url=https://www.britannica.com/event/Spanish-Civil-War |website=Encyclopædia Britannica |publisher=Encyclopædia Britannica, Inc. |accessdate=2025-03-11}}</ref>
, all stations served as air raid shelters. In 1936, the network had three lines operating, and over the next 10 years, development was reduced, although an increased growth rate of ridership can be observed. In 1944, a fourth line was constructed, absorbing and reusing a branch of Line 2. A decline can be noted from 1944, as WWII came to an end, national income fell <ref name="source10">{{cite web |author=Catherine Delano Smith |title=Spain - Franco’s Spain, 1939–75 |url=https://www.britannica.com/place/Spain/Francos-Spain-1939-75 |website=Encyclopædia Britannica |date=2019-02-24 |accessdate=2025-03-10}}</ref> followed by a slow recovery rate leading up to 1975 under Franco’s regime. In the early 1970s, the network expanded to cope with the influx of population and urban sprawl from Madrid’s economic boom, where new lines and larger platforms were developed to accommodate growth. <br />

The model of data from 1919-1973 represented in Figure _ results in an r-squared value of 0.962, meaning 96.2% of values fit in the regression model and the logistic curve has a strong fit. The t_nought value identifies the turning point/inflection point of this model, at approximately 1946, where growth decreases and approaches predicted maturity levels.<br />

[[File:Number of Passenger Journeys 1919-1973.png|'''Figure 3:'''Madrid de Metro: Number of Passenger Journeys 1919-1973|thumb]]<br />

'''Regression Results'''
{| table style="text-align:center;"  class="wikitable" border="1" cellpadding="4" cellspacing="0" style="border:\#c9c9c9 1px solid; margin: 1em 1em 1em 0; border-collapse: collapse;"
| align="center" style="background:#f0f0f0;"|'''Variable'''
| align="center" style="background:#f0f0f0;"|'''Value'''
|-
| K(S_Max)|| 530 
|-
| b|| 0.1111
|-
| t_i (tnought)|| 1945.7249
|-
| Intercept||-216.2993
|-
| R^2|| 0.9620
|}

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=== 1973 - 1987: Declining Trends ===
The death of Francisco Franco in 1975 marked the beginning of the Spanish transition to democracy <ref name="source10"/>. While the nation was experiencing political instability and violence levels grew, uncertainty was reflected in the decline of passenger demand of the metro. Affected by the political state of the nation, bad management of the metro system also led to a crisis, where ongoing projects ended up completing during the 1980s and all remaining projects abandoned. During this period, 100km of track was able to be completed, and by 1983, the suburban railway had also disappeared and converted to the new Line 10. However, recovery in passenger demand was not successful within this period of the system’s life cycle, as shown in Figure 4 below. 

[[File:Number of Passenger Journeys 1973-1987.png|'''Figure 4:'''Madrid de Metro: Number of Passenger Journeys 1973-1987|thumb]]<br />

'''Regression Results'''
{| table style="text-align:center;"  class="wikitable" border="1" cellpadding="4" cellspacing="0" style="border:\#c9c9c9 1px solid; margin: 1em 1em 1em 0; border-collapse: collapse;"
| align="center" style="background:#f0f0f0;"|'''Variable'''
| align="center" style="background:#f0f0f0;"|'''Value'''
|-
| K(S_Max)|| 22000 
|-
| b|| -0.0375
|-
| t_i (tnought)|| 1873.077
|-
| Intercept||70.1994
|-
| R^2|| 0.9317
|}
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=== 1987 - 2024: Recovery, Continued Growth & the Effects COVID-19 ===
In 1995, major expansion works began, developing 172 km of new line and 132 new stations completed and operating by 2011. Construction pace during this period was more than 10 km of new line per year ([[w:Madrid Metro|Madrid Metro]]), reflected in the positive trend shown in the S-curve below [23]. However, events including the Madrid Train Bombings (2004) <ref name="MadridTrainBombings">{{cite web |title=Madrid train bombings of 2004 |url=https://www.britannica.com/event/Madrid-train-bombings-of-2004 |website=Encyclopædia Britannica |publisher=Encyclopædia Britannica, Inc. |accessdate=2025-03-11}}</ref> and the financial crisis of 2008 and subsequently European debt crisis affected Spain particularly hard and put a pause on metro expansions as available funding dried up. Finally the rapid decline beginning in 2020 is clearly defined in ridership statistics<ref name="source4">{{cite web |title=In 2023, the number of Metro passengers increase by 16% in the Community of Madrid and comes close to the figures before the pandemic |url=https://www.metromadrid.es/en/press-release/2024-01-14/in-2023-the-number-of-metro-passengers-increase-by-16-in-the-community-of-madrid-and-comes-close-to-the-figures-before-the-pandemic |website=Metro de Madrid |date=2024-01-14 |accessdate=2025-03-08}}</ref> followed by the recovery, are both observable in the following figure. <br />

These fluctuations resulted in high uncertainty and caused a poor fit of the three-parameter logistic function as reflected in an r-squared value of 0.4143. Without including COVID years in the regression model, r-squared value was 0.7224, emphasising the high unpredictability during the COVID-19 pandemic.<br /> 

[[File:Number of Passenger Journeys (1987 - Present).png|'''Figure 5:'''Madrid de Metro: Number of Passenger Journeys 1987 - 2024|thumb]]<br /> 

'''Regression Results'''
{| table style="text-align:center;"  class="wikitable" border="1" cellpadding="4" cellspacing="0" style="border:\#c9c9c9 1px solid; margin: 1em 1em 1em 0; border-collapse: collapse;"
| align="center" style="background:#f0f0f0;"|'''Variable'''
| align="center" style="background:#f0f0f0;"|'''Value'''
|-
| K(S_Max)|| 22000 
|-
| b|| -0.0375
|-
| t_i (tnought)|| 1873.077
|-
| Intercept||70.1994
|-
| R^2|| 0.9317
|}
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== '''Conclusion''' ==
The Madrid Metro serves the capital of Spain well as a core network for connectivity of its population. The overall shape of passenger journey data over the entire lifecycle is not smooth. Experiencing several declines and re-growth, from events such as the end of the Franco Regime (1975), Global Financial Crisis (2008) and COVID-19 Pandemic (2020), it can be said that due to policies reflecting historical periods of Madrid, direct impacts to developments of the rapid transit system is visible. Model 1 and Model 2 relatively accurately estimate birth, growth and maturity, and declining phases of Madrid’s Metro system respectively. However, Model 3 proved difficult to predict what is to come for Madrid’s Metro system. Madrid Metro will remain as one of the most advanced transit systems in Europe and continue to adapt to sustainability, environmental and mobility needs of Madrid and its people. From previous data, trends and analysis, ridership and passenger journey levels should recover from COVID-19 declines and continue to show growth. 
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==References ==
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