the connection-count test

As I look at the new metros being built in the developing world, I'm noticing some striking connection-count problems.  Consider Delhi, a city I know a bit:

Delhi metro frag

The full Delhi Metro network map is here, but this slice is the only part of the system where lines connect with one another. 

What's wrong with this picture?  Well, suppose you want to go from Shivaji Park, on the green line in the upper left of the image, to Khan Market, in the lower right.  That's right: three connections.

Developing a new metro in a crowded city is always an exercise in compromise, but I'm struck by how often one of the first compromises is network integrity, easily measured in the reasonableness of the number of connections required. 

In an idealised grid network, the maximum number of connections for almost any trip is one.  Plenty of real-world networks require two connections for a range of trips between secondary stations.  But requiring three is pretty remarkable. 

30 Responses to the connection-count test

  1. In Brisbane February 3, 2011 at 3:11 am #

    I’m just amazed that their metro is so extensive, wow, what is the cost per kilometre to build that? We, over here, just talk about metros, over there they build them!
    Rumour has it that the metro is profitable? Is that correct?

  2. John February 3, 2011 at 5:23 am #

    It almost looks like they’re trying to avoid having overlapping routes for some reason. Without knowing the details of their track configuration, it seems that this particular connection problem could be solved by interlining the green line and the dark blue line over the orange and red lines. DC does a nice job of this.

  3. marco February 3, 2011 at 5:41 am #

    In Rome is pretty the same: 3 over 5 lines have just one connection, and most trips have to pass through “Termini”.

  4. Tom West February 3, 2011 at 6:42 am #

    For London Underground, each line intersects most of the other lines, and where two lines don’t intersect, there is always a third which intersects both… meaning that despiote its chaotic apearence, two changes is alwasy sufficient. (Although a third sometimes makes things quicker).

  5. Bossi February 3, 2011 at 6:54 am #

    I definitely do not know Delhi… but my first question is what’s the actual demand to travel between Shivaji Park & Khan Market? If it’s only a couple riders per day, I wouldn’t find myself becoming too concerned about it; and with time each location may come to develop its own services, residents, and workforces such that they may become even less relient on one another.

  6. Christopher Hylarides February 3, 2011 at 7:24 am #

    “Well, suppose you want to go from Shivaji Park, on the green line in the upper left of the image, to Khan Market, in the lower right. That’s right: three connections.”
    The real question is this: are a lot people actually moving this way or were the lines reacting to movement of people elsewhere?

  7. Tobias February 3, 2011 at 7:45 am #

    @ Jarrett
    In an idealised grid network, the maximum number of connections for almost any trip is one.
    In an orthogonal grid network many trips require two interchanges actually as lines run parallel to each other and never intersect.
    As for Delhi, their metro network is still developing. At this premature stage coverage has certainly the greatest priority. Once the blue and the green lines are extended, the numbers of necessary interchanges are cut automatically.

  8. Alan Robinson February 3, 2011 at 8:30 am #

    @ Tobias
    “In an orthogonal grid network many trips require two interchanges actually as lines run parallel to each other and never intersect.”
    This is not a problem in an ideal grid where every destination is within walking distance of both a north-south and an east-west line.

  9. GT February 3, 2011 at 8:34 am #

    @John: DC does interline their Orange and Bblue lines downtown, but this cuts the capacity of each line severly outside of the interlined section. We call the Orange line at rush hour the ‘Orange Crush’. It saved a huge amount of money to build it this way, but 30+ years later it’s a significant limit on the system’s capacity.

  10. John February 3, 2011 at 8:45 am #

    @In Brisbane,
    The DMRC website gives the Phase 1 project cost as “Rs.10, 571 crores.” Internet research found that a crore is 10 million. So it’s 105,710,000,000 rupees, which is currently equal to about $2.3 billion in USD or AUD. Phase 1 will be 65 km, so the cost per kilometer is only $35.7 million/km, or 57.5 million/mile. That’s crazy cheap, like maybe cheaper than light rail here.

  11. John February 3, 2011 at 8:51 am #

    Are you suggesting that the orange line should only run between Vienna/Fairfax and Rosslyn or between New Carrollton and Stadium-Armory so it can run more frequently? Wouldn’t this just result in everyone trying to transfer onto crowded blue line trains and you’d have a blue crush with the same number of passengers through the corridor? Or are you saying land use would change over time to make Rosslyn and Stadium-Armory hubs so fewer people would travel through? It sounds to me like you need four tracks.

  12. Jeff Wegerson February 3, 2011 at 9:06 am #

    Off topic
    For your “amusement”:
    During a recent snow event in Chicago some buses got trapped amongst hundreds of cars in snowed-in traffic for hours.
    The winds were fierce coming off of Lake Michigan so eight lane Lake Shore Drive became more of a challenge than many expected. Oh for a dedicated bus lane!
    Here’s a photo of rescue in progress ->,0,6310905.story
    and here’s a bus that probably couldn’t get the door closed after rescue ->

  13. anonymouse February 3, 2011 at 10:35 am #

    @John, I think ideally, the Orange Line would run from Vienna to New Carrollton and Largo, with the Blue Line not sharing the Rosslyn tunnels at all. WMATA actually had a proposal to divert half of the Blue Line trains via the Yellow Line, and there have been proposals to build a new line from Rosslyn to Georgetown and north of the existing Orange/Blue trunk to Union Station, in order to give the Orange Line an exclusive path into DC.

  14. John February 3, 2011 at 10:47 am #

    Thanks for the details. I don’t know much of anything about the specific ridership on different branches of the DC Metro that would determine the optimum configuration, but I think the point about the original point about the good connectivity of the network to enable single transfers (sorry Jarrett) rides remains.

  15. Tobias February 3, 2011 at 10:52 am #

    @ Alan
    This is not a problem in an ideal grid where every destination is within walking distance of both a north-south and an east-west line.
    This is a rather uneconomic approach and therefore far from ideal. I have no idea how densely a city has to be populated to sustain such a close-meshed network.

  16. Tim Gould February 3, 2011 at 1:00 pm #

    It somewhat depends on how quick the connections are IMO. Sure it would be ideal to only make one connection but if it’s simply a matter of getting off one train and crossing a platform it’s not a big deal. People do that on the Tube all the time to make a journey quicker.
    Whereas many Tube transfers might technically be in the same station but your interchange time can be huge. Two quick transfers would be far superior.

  17. Zoltán February 3, 2011 at 4:40 pm #

    Oh, the orange line is such great fun at rush hours.
    My (relatively) low-cost solution to the orange line problem, specifically designed to make the silver line work, is this:
    – Blue line abolished in current form. Orange+silver line run every 3 minutes, enhancing frequency between West Falls Church and gold line (see below) interchange station at River Terrace.
    – New Gold line light rail. As per H St NE/K St NW streetcar but with reserved lane, then through Georgetown M St and Francis Scott Key Bridge in reserved lane, shallow tunnel through Rosslyn, former blue line Arlington Cemetery Line, new Pentagon station and running beside rail ROW to terminate at Crystal City. Designed for signal priority and long trains to provide high speed and capacity.
    – Support 4-tracking of MARC Penn Line, extension of MARC train to Northern Virginia with four-tracking from L’enfant to Alexandria, high platforms and related improvements, and integrate fares with metro.
    – Commuter rail takes over former Blue Line alignment Alexandria to Franconia-Springfield, providing 8tph peak and 4tph off-peak at Franconia-Springfield and Van Dorn Street.
    – 4tph Penn Line service at peak times, providing relief at New Carrollton.

  18. Matt February 3, 2011 at 5:59 pm #

    I dealt with some of these issues recently when developing a long range plan for a transit network. While the ideal network may have been a grid or bent grid, there were a few reasons why this wasn’t pursued. These included:
    – existing infrastructure and services
    – unbalanced demand
    – differing customer markets and requirements
    – constraints related to natural geography and the location of existing employment centres
    – potential for transit-oriented development
    – community and political priorities
    This can lead to a network which is not ideal from an sim-city viewpoint. This can be overcome by designing in flexibility to adapt the network over time to re-route lines or allow efficient interchanges as the network grows. However, even these relatively small investments in future flexibility also add to up-front project costs which are heavily penalised in an economic analysis with discounted cash flows.

  19. Alon Levy February 4, 2011 at 12:46 am #

    @In Brisbane, John: the cost of the Delhi Metro is actually quite high. First, bear in mind the system is predominantly above ground. Second, in PPP terms, you need to multiply the exchange rate figures by 2.8, so that the cost is about $100 million per km, comparable to or higher than fully underground subways in such first-world countries as Italy, Spain, and South Korea.
    @Jarrett: the Green Line is incompatible with the Red Line – it uses standard gauge instead of Indian gauge. I’m not sure why it’s so, but it’s not unheard of for cities to have some branch lines that use lighter technology (often shorter platforms) than the mainline and as a result don’t run through. For examples, Line 5 in Shanghai, Line L1 in Moscow, the Batong Line in Beijing, and the Yellow Line in Chicago.

  20. EJ February 4, 2011 at 6:38 am #

    @John, Zoltan
    Metro’s long-term solution, which the transit-heads at Greater Greater Washington mostly like, is a redundant crosstown subway for the blue line:
    New tunnel from Rosslyn to Wisconsin & M (Georgetown). Across M Street through downtown (connecting to Red, Yellow, and Green along the way), to Union Station, and then to H Street NE and a new River Terrace stop.

  21. M1EK February 4, 2011 at 8:49 am #

    Now wait just a minute. I’m pretty sure the talking point spread here by most people is that timed cross-platform transfers have no impact on ridership. What has changed?

  22. Zoltán February 4, 2011 at 9:25 am #

    @EJ I’ve seen that plan, but I can’t help but think that:
    – It needs to happen now – subways take a bloody long time to get built, and streetcar tracks are already in place in parts.
    – With 400-600m stop spacing, the streetcar is designed to be quite quick. They clearly have rapid transit in mind.
    So I stand by it being a better solution to get the gold line as described now, and to take as long as they need over building tunnels for that route and stops – tunnels to link up with the bits that would have to be tunnel from the outset at Rosslyn and Union Station.

  23. Alon Levy February 4, 2011 at 3:27 pm #

    @M1EK: I’ll take the bait and say that I doubt that the Delhi Metro uses timed cross-platform transfers anywhere. If you know otherwise, let me know.
    The system with branch lines I’m most familiar with, Singapore, does not time the transfers, and does not use cross-platform transfers except between the North-South and East-West lines.

  24. bzcat February 4, 2011 at 4:20 pm #

    This is not just a problem with metro system in developing world. It’s a big problem in supposedly developed country. 3 connections is a fact of life in Los Angeles too.

  25. Andrew February 4, 2011 at 7:40 pm #

    This is a problem in China as well. Several lines are split into two, an outer suburban line and an inner city line, with a mandatory transfer between the two lines at an intermediate station. For instance in Shanghai line 5 is a continuation of line 1, and line 2 is split in two at Guanglan Road. In Beijing the Batong Line, Fangshan Line, Daxing Line and Yizhuang Line extend lines 1, 9 (still under construction), 4 and 5 respectively. Madrid also has several lines split into two sections like this.

  26. Joseph E February 5, 2011 at 9:03 am #

    Los Angeles currently has a gap in the planned light rail system, right in Downtown LA, which requires everyone to transfer to the heavy rail subway or a bus in mixed traffic. This adds 15 to 20 minutes to every trip thru downtown, compared to the planned system after the “regional connector” is finished.
    Consider this trip between a station on the first Downtown station on the Blue Line and one on the Gold LIne (which my wife was considering for a job recently), which requires 2 connections to be done by rail, or 1 by bus. Walking would only be 3 miles and take about 1 hour, while the train takes 43 minutes, plus an average of 5 to 10 minutes waiting time. Clearly bicycling is the best option. Map:
    A similar trip to the Chinatown station likewise takes 36 minutes of transit time, or an average of 40 to 45 minutes total without walking time, while walkind directly would take and hour and 5 minutes. Map:
    The Regional Connector will allow trains to run thru on this section, reducing trip times by 15 minutes (or more, evening and weekend) for both of these trips. It was originally planned as part of the Blue Line back in the 1990’s, but money ran out at the time.

  27. M1EK February 7, 2011 at 7:46 am #

    @Alon, I’m happy to bait you but don’t accept homework. You’re the one who assures us it’s trivial to develop networks with timed cross-platform connections between rail lines, so I naturally assumed this system had them.
    Remember, I’m the transfer skeptic. And most of the time on this site, it’s a lonely place to be.

  28. Zoltán February 7, 2011 at 9:14 am #

    Yes, of course, you’re the transfer skeptic. I take no issue with a distaste for transfers; transfers are not that fun. I would be in full agreement with you on that.
    I do, live in Leeds, where routes try very hard indeed to all go downtown, so I’m very familiar with networks that result from being skeptical about transfers.
    My nearest bus route duplicates others for all but a mile of its journey into central Leeds, and in the course of that mile makes six turns, all of which involve yielding to another traffic flow, and takes about ten minutes to accomplish the distance. This despite spending much of that mile on two roads that are both quite useful to cars and bicycles making crosstown trips that no buses offer.
    Meanwhile, when I want to go somewhere other than central Leeds, it’s made really difficult – and expensive, as free transfers aren’t offered. I have to either:
    a) Waste 10-20 minutes backtracking downtown, or more if the buses take different routes through downtown and never intersect.
    b) Make up to two transfers, the first of which involves waiting for the one and only crosstown route that runs more once in hour – it runs twice an hour, in fact.
    c) Take a radial route a bit of the way, then do a lot of walking.
    d) Not make the trip at all.
    c) and d) are the options I most commonly choose.
    And herein lies the problem. Being skeptical of transfers tends to produce a network that’s sort-of-alright for going downtown, and no use whatsoever for anything else. Minimise transfers as far as practicable by all means, but it’s no substitute for making them work well when they’re necessary.

  29. Alon Levy February 7, 2011 at 3:45 pm #

    Just because timing transfers is easy on legacy mainline networks (but not so much on subways) and generally desirable doesn’t mean everyone does it.

  30. Nathan February 7, 2011 at 9:25 pm #

    When San Francisco Muni redid the transit system in the 1970’s, the goal was to make it possible to get anywhere in the city with only one transfer. With a few hillside exceptions, they succeeded and the system has been generally maintained. Admittedly, San Francisco is relatively small, roughly 7 miles (11 km) square. But that single transfer hadn’t previously existed, and some lines had to be extended to curve around the city, run through new neighborhoods.