This is the start of a series of posts on “basics,” by which I mean “things you really need to understand about the geometry and economics of transit if you want to form intelligent opinions about it.” These will tend to be longish logical arguments, but they’re intended to make sense to any reasonably smart person; please tell me if they don’t.

To complete your trip in a world-class transit system, you may have to make a connection, or “transfer” as Americans say. That is, you may have to get off one transit vehicle and onto another. You probably don’t like doing this, but if you demand no-transfer service, as many people do, you may be demanding a mediocre network for your city.

There are several reasons for this, but let’s start with the most selfish one: your travel time.

Imagine a simple city that has three primary residential areas, along the top in this diagram, and three primary activities of employment or activity, along the bottom.

In designing a network for this city, the first impulse is to try to run direct service from each residential area to each activity center. If we have three of each, this yields a network of nine transit lines:

Suppose that we can afford to run each line every 30 minutes. Call this the Direct Service Option.

Now consider another way of serving this simple city for the same cost. Instead of running a direct line between every residential area and every activity center, we run a direct line from each residential area to one activity center, but we make sure that all the resulting lines connect with each other at a strategic point.

Now we have three lines instead of nine, so we can run each line three times as often at the same total cost as the Direct Service option. So instead of service every 30 minutes, we have service every 10 minutes. Let’s call this the Connective Option.

Asking people to “transfer” is politically unpopular, so the Direct Service option is the politically safe solution, but if we want to maximize mobility with our fixed budget, we should prefer the Connective option. Consider how long at typical trip takes in each scenario, from the standpoint of a person whose needs to leave or arrive at a particular time.

Let’s arbitrarily look at trips from Residential Area 1 to Activity Area 2. For simplicity, let’s also assume that all the lines, in all the scenarios, are 20 minutes long.

In the Direct Service scenario, a service runs directly from Residential Area 1 to Activity Area 2. It runs every 30 minutes, so on average, the waiting time is 15 minutes. Once we’re on board, the travel time is 20 minutes. So the average trip time is:

Wait 15 minutes

+ Ride 20 minutes

= 35 Minutes.

Now look at the Connective Option. We leave Residential Area 1 on its only line, which runs every 10 minutes, so our average wait is 5 minutes. We ride to the connection point and get off. Since this point is halfway between the residential areas and the activity centers, the travel time to it is 10 minutes. Now we get off and wait for the service to Activity Area 2. It also runs every 10 minutes, so our average wait time is 5 minutes. Finally, our ride from the connection point to Activity Area 2 is 10 minutes. So our average trip time is:

Wait 5 minutes

+ Ride 10 minutes

+ Wait 5 minutes

+ Ride 10 minutes

= 30 minutes.

The Connective Network is faster, even though it imposes a connection, because of the much higher frequencies that it can offer for the same total budget.

As cities grow, the travel time advantages of the Connective Network increase. For example, suppose that instead of having three residential areas and three activity centers, we had six of each. In this case, the direct-service network would have 36 routes, while the connective network would have only six. You can run the numbers yourself, but the answer is that the Direct Service network still takes 35 minutes, while the Connective network is down to only 25 minutes, because of the added frequency.

Common Objections

Lets anticipate a couple of objections to this thinking:

The Modeler’s Objection

If we were actually using travel time as a means of estimating ridership, we would have to consider the widespread view, built into most ridership models, that connections impose a “transfer penalty” in addition to the actual time it takes. These penalties assume that even though people say they want the fastest possible trip, they’ll actually prefer a slower trip if it saves them the trouble of getting out of their seat partway through the journey.

In the above example, for example, a model might assume that although the average trip in the Connective option is faster, the Direct Service option would give us higher ridership, because the Connective option imposes the inconvenience of the connection. The modeler might say that this inconvenience is the equivalent of 10 minutes of travel time, so that the Connective option will really attract ridership as though the trip took 40 minutes instead of 30. This common modeling approach assumes that the inconvenience of transferring is something different to, and separable from, the time that the transfer takes.

There is considerable documentation behind the addition of this kind of factor, but the unpleasantness of the connection experience depends on many details of how the connection works. If two buses or trains arrive on opposite sides of a platform, facing one another five meters apart, with their doors open at the same time, walking out of one and into the other is a pretty low level of inconvenience for most passengers. If the connection involves getting off a bus, crossing a busy street, and waiting for another bus not knowing when it will arrive, the inconvenience is much greater.

So the configuration of the connection matters. Transfer penalties are based on a crude averaging of many different types of connection experience, so good interchanges will reduce these penalties. Modeling assumptions about a “transfer penalty” (as distinct from the time the connection takes) deserved to be scrutinized: What kind of connection experience was used to calibrate the model?

The 9-to-5 Commuter’s Objection

Many people who make regular commutes would object to the way I’ve inferred average waiting times from frequencies. After all, if a particular airline route has one flight a day, that doesn’t mean we have spend half the day waiting for it. We go on with our lives and work, and go catch the flight whenever it is going. Many people do treat commuter service schedules in this way. Even if the bus runs every 30 minutes, they’ll just do other things until it’s due, and then go out to catch it.

However, the average wait is still a valid way of capturing the inconvenience of low-frequency services. For example, if you need to be at work at 8:00 and your bus is half-hourly, you may have to take a bus that gets you to work at 7:35. This means that every morning, you’ll have 25 minutes at your destination before work starts, time you’d probably rather have spent in bed. You may figure out how to make use of this time, but it’s still time you must spend somewhere other than where you want to to be.

Note too that for simplicity we have presented this example in terms of commutes to work, but of course, a good public transport system serves many kinds of trips happening all day. You may figure out how to make use of a predictable 25 minute delay at the beginning of your work day, but it’s much harder to deal with unpredictable 25 minute gaps in the many trips that you need to make in the course of the day, such as while taking a lunch break or running errands that involve many destinations. So all-day frequency still matters.

Other Advantages of Connective Networks

Several factors that argue for Connective networks over Direct Service networks.

Average travel time is better than the worst-case time calculated above. In the Direct Service network, everybody’s trip takes 35 minutes. In the Connective network, two-thirds of the market has a 30-minute trip, but one-third of the market (those still served by a direct route) have an even faster trip.

The Connective network is made of more frequent services. Frequency makes connections faster but it also stimulates ridership directly, especially when we consider the needs of people who have to make several trips in a day, or who want to travel spontaneously, and who therefore need to know that service is there whenever they need it.

The Connective network is simpler. A network of three frequent lines is much easier to remember than a network of nine infrequent ones. Marketing frequent lines as a Frequent Network can enhance the ridership benefits of this simplicity.

This last item is so important that I’ll do another post on it soon.

Most transit networks start out as Direct Service networks with relatively little focus on connections, but as the city grows bigger and more complex, connections become more important. In most cases, though, there’s a transition from a Direct Service network to a Connective one, a transition that often requires severing direct links that people are used to in order to create a connection-based structure of frequent service that is more broadly useful and legible.

Helping agencies through this hard step is one of my specialties as a consultant, and while there’s usually a moment in the process where the resistance seems overwhelming, the agencies I’ve worked with are almost all glad that they broke through this resistance, because the result was a network that was much more frequent, and therefore more relevant to the life of the city.