14 Dec 2013

World Metros, Subways and Undergrounds

What are the oldest, most crowded, or expensive: Subways, Metros or Undergrounds in the world? The first Underground passenger transport system was built in London in the 1860's and continues in operation today. Soon after, in the same decade, the New York Subway started operations. Other cities joined the party in the 1900's. During the 60's and 70's major developments took place around the globe, large metro networks of today were born during that time (Mexico City Metro, Beijing Subway, Seoul Metropolitan Subway). Every year since then, new Metros, Subways and Underground systems are built and old networks expanded. The next figure is of great help to visualize this global phenomena. The graph includes the opening year and the year of the last expansion, from the oldest metro system to the newest one (as for today 11/12/2013, data for all figures in this post was gathered from different sources).

The oldest and the newest Underground, Subways and Metro systems of the world
Oldest: 1) London, 2) New York. Newest (as for 2013): 1) Fortaleza, 2) Suzhou.

Growing cities and population demand for efficient transport systems such as Metros, Subways, etc. Their networks satisfy this demands by expanding the number of stations and route length as the cities grow. Thus, this transport systems are dynamic and change with time. Major investments are also required and not all cities of the world can afford the same type or extent of network. However, it is possible to look at these factors in the time window of today. The figure below shows the total number of stations, users per year, and route length in km for all the metro systems of the world.

The longest Metros, Subways and Underground networks, with the most stations and users per year
Top 11 by users per year: 1) Seoul, 2) Moscow, 3) Beijing, 4) Shanghai, 5) Tokyo, 6) Guangzhou, 7) New York, 8) Mexico City, 9) Hong-Kong, 10) Paris, 11) London.
Top 11 by network length: 1) Seoul, 2) Shanghai, 3) Beijing, 4) London, 5) New York, 6) Berlin, 7) Moscow, 8) Madrid, 9) Guangzhou, 10) Mexico City, 11) Paris.
Top 11 by number of stations: 1) New York, 2) Seoul, 3) Shanghai, 4) Paris, 5) Madrid, 6) London, 7) Beijing, 8) Mexico, 9) Moscow, 10) Tokyo, 11) Berlin.

It can be noticed immediately that there are variations in the number of stations and number of users for all systems. One of the questions that immediately arises is what are the most crowded Metro systems of the world. This can be answered in terms of users per km of network or users per station with the figure below. Of course this is just an estimation and you don't want to be in the most crowded station of the world at peak times, the next figure may guide you (divide by 365 for a daily estimate).

Millions of users/year per km of network and per station, for all Metro systems of the world.
Top 5 crowded per station: 1) Hong Kong, 2) Cairo, 3) São Paulo, 4) Guanzhou, 5) Moscow. Bottom 5: 1) Fortaleza, 2) Palma, 3) New York, 4) Mecca, 5) Cleveland.
Top 5 crowded per km: 1) Cairo, 2) São Paulo, 3) Tokyo, 4) Prague, 5) Budapest. Bottom 5: 1) Fortaleza, 2) Palma, 3) Cleveland, 4) New York, 5) Mecca.

Here is a good time to give a recognition to the New York Subway; despite its high ridership, it manages to provide a not so crowded ride. It is important to notice here that the users per km per year is a good indication of the people being carried in a given metro, subway, or underground train; and this may vary drastically if the number of trains per line or km is not sufficient. Here it is assumed that they are evenly distributed (i.e. trains/km equal for all Metros of the world, obviously they are not, that data is lacking here). What it is not lacking and can be certainly evaluated is how the number of stations per kilometer is distributed globally. Certainly someone thought about an optimum for a radially expanding city. The figures below shows this correlation, its distribution and the annual ridership for reference.

There is a global correlation for the number of stations per km of route length
There are approximately 1.16 km added for each station. Or in other words for every new 1.16 km of network a station seems to be required (a global trend).

The statistics show that in fact most Metro systems have stations within walking distances (in average)
Tokyo, São Paulo, Mexico City and Cairo fall in the average of 0.86 stations per km. However, you would not like to walk from station to station in San Francisco, Hong Kong or Beijing. This might no be a problem in Lausanne or Paris or New York, where you can find stations within walking distances (in average).

That is all fine, but there is obviously a difference when it comes to infrastructure, new networks will be faster and efficient, whereas old networks may require investments in modernization, etc. Developed economies may have procedures in place to do this on a yearly basis. Other not so developed economies may struggle to increase the fares and modernize their networks due to population complains. Thus, it is all about the money, but how expensive is to ride the Metro, Subway or Underground around the world? The figure below shows the fares (equivalent in USD) for a one trip ride, for the longest possible distance at any time, and without discount fares (i.e. multi-tickets, discount cards, etc. just plain single fare to travel the longest possible way).

Fares for all Metro, Subway, Underground systems of the world
Most expensive: 1) Mecca Metro, 2) Staten Island Railway, 3) Copenhagen Metro
Cheapest: 1) Pyongyang Metro, 2) Tehran Metro, 3) Maracaibo Metro

The annual users and the price of the ticket are definitely not in good agreement, but it is a good indication of how much the Metros, Subways and Undergrounds earn per year from ticket sales. One would expect this to be related to the wealth of the country as well as to the extent of the network (requiring more money to maintain larger networks). To avoid speculation, the gross annual income (estimated by multiplying the price of a single fare times the annual ridership) is plotted against network length in km in the figure below.

Annual income from ticket sales (assuming 1 user, 1 single ticket)
The most profitable metros seem to be London, Tokyo and Toei. It is difficult to visualize the less profitable ones from this figure since most of them fall on the bottom right of the plot. It can be immediately noticed how some metros are heavily subsidized or run with suboptimal earnings (e.g. Mexico City, Cairo, Tehran, Delhi, large circles towards bottom right). There seems to be a correlation of  100M USD for every 80km of network added.

A question that immediately arises is how much is the Metro, Subway or Underground system earning per km per year with the previously stated assumptions. This is also a indication of how much the users can afford to pay in a given country or city. The figure below shows this.

Annual income per kilometer of network (in million USD/km, assuming 1 user, 1 single ticket)
Earns the most per km: Copenhagen, Earns the less: Pyonyang.

The figure below shows the fare per km of network. The data points are ordered by annual income. A question that can be asked now is for an increasing demand (i.e. number of users) what is the minimum amount that can be charged? Next figure gives a hint.

Cost per kilometer for all Metros, Subways and Underground systems of the world
The trend given by the colors shows that the fare per kilometer decreases as the number of users increases. This may prove once again that with increasing demand the price decreases. There seems to be an optimal minimum value of $0.002 USD per kilometer, as shown by the Metros with the most users: Seoul, Beijing, Shanghai, and Moscow (the global average is $0.09 with median of $0.03)

Conclusions and the future:
In planet Earth the Metro costs $0.009 per kilometer and there is one station for every 1.16km of network. There are currently 9328 stations in the 11369km global network serving 47875 million users per year. The networks is expanding exponentially at a current rate of 74 km/year, and 313 million users/year. It is expected to reduce the current price to $0.002 and to have one station every 800m in crowded areas (>2B users/year). We are currently working on an integrated network map with airport and/or rail connections. Welcome to planet Earth!