Sunday, June 15, 2014

Buses' mediocrity dilemma: why buses can't compete with cars

I spoke earlier of how important speed is in determining what mode of transport is dominant and how it will shape the developments that will grow in an area. But in determining the ability of a transit line to attract users, there are actually two main factors:
  1. The average speed of the line (commercial speed)
  2. The frequency of the line
If we suppose that people randomly need to go to certain places, meaning they do not choose the moment of their departure, the time to reach the destination is not only the time required while in the vehicle, but the time to get to the stop and spent waiting at it. That waiting time can be estimated at half the frequency of the line, so if there is one vehicle per 10 minutes on a line, the average waiting time should be 5 minutes. This would include the waiting time at home if the schedule of the line is known for the user.

The frequency of a transit line is primarily the result of the capacity per vehicle and the ridership of the line. The more riders a line has, the more it justifies putting an higher number of vehicles running on the route, increasing frequency.

For example, if a transit agency has a standard of offering one bus per 40 passengers in the hour on a line, then we can draw a graph illustrating how the frequency of the line will vary depending on the number of passengers on the line per hour. It would look like this:

Graph illustrating the relation between frequency and ridership
So considering that the waiting time is half the interval between vehicles, it looks like a virtuous circle. The more riders there are, the higher the frequency. The higher the frequency, the shorter the waiting time. The shorter the waiting time, the faster the trip will be. Great, right?

Unfortunately, that is not quite accurate, at least, not with regular local bus service (streetcars have the same issue most of the time).

The problem is that these lines are characterized by a great number of closely spaced stops, around 200-250 meters between each (1/8 of a mile). The stop spacing has a great influence on the speed of the vehicle while it is in movement. By supposing an acceleration and deceleration of 1 meter per second squared (a decent estimate to insure comfortable accelerations and decelerations for users) and a certain time stopped at each stop (including stops due to stop signs and traffic lights), we get the following curves representing the average speed of vehicles depending on how far they can go without stopping on average. Each curve represents a different maximum speed.

Average speed of a transit line versus the average distance between stops

For miles per hour, divide by 1,6.

OK, a bus can still get a decent speed despite a great number of bus stops if most of these are unused, as it doesn't need to stop at each bus stop, only at those where people get in or get out. That means that the less people per kilometer board or get off the bus, the faster the bus will go.

Oops. This is no longer a virtuous circle here! The higher the ridership, the slower the bus will go. If I model this dynamic, supposing a bus route on urban streets where normal vehicles go at an average of 23 km/h (15 mph), this is what I get.
Average speed of urban buses versus the number of boarding per km, supposing bus stop spacing of 200 meters

Now, this was in a rather urban area with a lot of stops and traffic lights will slow down all vehicles, but even then, with even just 3 boardings per km, the bus will move around 40% slower than cars. This is also true for suburban buses on roads with few stops and lights.
Average speed of suburban buses versus the number of boarding per km, supposing bus stop spacing of 200 meters

So that creates a big problem for local transit lines, a dilemma if you will:

1. If ridership is high, then the waiting time will be short, but it will take more time getting anywhere on the bus as it will be slower
2. If ridership is low, then the waiting time will be high, but once on the bus, the speed will be similar to that of cars taking the same route

So in either cases, this is an inescapable pit of mediocrity compared to cars' speed. Either frequent and slow or infrequent and fast, but never frequent and fast. That's why these local transit lines traveling next to cars can never really contest the domination of cars. And in urban settings, often biking will be faster than buses, so in a walkable, bikable dense city, buses are virtually useless for most people.

Note that the reality is even worse than that, as bus drivers are on a schedule, and the only way to maintain that schedule is to build in excess time so that buses can catch up to the schedule if there are more passengers than expected. What this means is that if there are less passengers than expected, bus drivers will slow down not to arrive too quickly to the next stop, since being late is one thing, but being too quick is more than just a little annoying to transit users who see the bus passing before them as they're walking to the stop.

What this underlines is the importance of rapid transit investment with grade separation so that transit can be at the same time high-capacity and high-speed, which is necessary to compete effectively with cars. To satisfy oneself with simple buses running on shared streets is to be satisfied with transit remaining a marginal mode of transport which will take 2 to 3 times more time to get anywhere, in the best case scenario.

Mitigating measure

This problem can be somewhat mitigated, but never eliminated, by eliminating bus stops and thus having a greater stop spacing. This way, you can cap the amount of time buses will have to stop to pick up or let off passengers even if ridership increases. As the buses stop less often, they can maintain their speed better.

Average speed of an urban bus line depending on boardings and stop spacing
This way, by eliminating half the stops, we can save a transit rider making a 8-kilometer trip 5 minutes in the bus. This can even reach 7 minutes if we eliminate 2 stops out of every 3. However, the gains of this method are insignificant for poorly used bus lines, like most suburban bus lines. Ironically, this means that stop spacing in urban neighborhoods, where more people are likely to use transit, should be greater than in suburbs where transit is only rarely used.

Greater stop spacing does mean that people will have to walk greater distances, but it's a trade that's worth it if the goal is to make transit a competitive way of getting around and to increase ridership rather than to perpetuate the conception of transit as a form of welfare program made exclusively for those too young, too poor, too old or too sick to drive.

As an added bonus, if buses are faster, as most of the cost of running them is in the form of wages, it means that their costs tend to be proportional to their time running rather than distance traveled. So if you speed up buses, that means that you can increase the frequency of lines for a negligible increase in costs as the buses finish their routes faster and thus can be sent back to do another route quicker. If you can afford 4 separate buses on a route and this route takes 40 minutes to run, then that means each bus can only do 1,5 time the route each hour, for a frequency of one bus every 10 minutes, 6 buses in an hour. But if you speed up the buses by 30%, then the route takes only 30 minutes to do, the same 4 buses can do the route twice every hour, for an interval of 7,5 minutes between buses, with 8 buses an hour from the point of view of riders. This increases frequency and capacity of the line, all for a minimal additional cost (mostly gas).


  1. I'm not sure I understand how higher ridership means more stops. What are we assuming here? Is the difference between the low and high ridership route how full individual buses are, or is it the number of buses per hour? I would think the likelihood of skipping stops depends on passengers per bus, but not buses or passengers per hour.
    Anyways, the speed of the vehicle is not the only thing that matters, but how long it takes to get there, how long you wait, and how long you walk to the final destination.
    Let's say you live in an urban neighbourhood (23km/h vehicle speeds), and there's a fast bus route (18km/h) and a slower one (14km/h) with stop spacing of 1000m and 200m respectively. With 200m spacing, you walk less, and to make up for that, you’d have to travel about 5km on the 18km/h bus. Certainly there are people who would travel over 5km, but in an urban neighbourhood, you'd still have quite a few trips that are shorter, so it could make sense to have both local and express buses.
    In a suburban neighbourhoods, buses can travel faster, which means the net difference in speed is more affected by how often it stops. Plus things are further apart, so you're more likely to have longer trips. Greater stop spacing therefore make more sense.
    And regarding "choice" riders... I don't really like looking at it that way. Car related expenses are pretty high. Even lower density areas where parking is cheap (both at the origin and destination), it's around $6,000-$10,000/year per car. So you're looking at $5000/year in savings, and possibly thousands more if you have to pay for parking. That's $15/day. That means someone making minimum wage could potentially be willing to spend 90min more per day commuting by bus vs driving*. An extra 20min/day means commuting by bus means it would still be worth it for someone making $45/hour. And honestly even a high paid person might rather be paid $45/hour to sit on a bus than spend it on stressful overtime work. With short trips, it’s easier to get down to a 10-15min difference (ie 15 vs 30min is easier to achieve than 45 vs 60min).
    Also, this assumes the new transit user will be giving up a car. If you already own a car, a lot of that's a sunk cost**... so it's much more difficult for transit to be competitive, almost impossible, except maybe in very special circumstances, like for subways/commuter rail to downtowns of large, dense, congested cities. But if there's a 2 car household and one car breaks down, you'd have a decent chance at getting them not to buy a new one and switch to transit. Or a university graduate who finally gets a decent paying job, and is trying to decide if they want to buy a car or stick with transit and spend the money on other things.

    I guess my main point is there isn't some quality threshold where suddenly you get all the choice riders on board. Any improvement will yield increased ridership. It's more about decreasing the difference in travel time than eliminating it.
    I agree using various measures to give transit an advantage over cars is a good way to achieve that, whether that's a dedicated ROW or signal priority. In suburban areas, signals often have a rather long cycle length, especially on those big high volume 6 laners. Jarrett Walker has often said that the usefulness of transit is that it takes up less space. That means it can reduce congestion/increase capacity of a road/corridor. But that only works if people use it, and for people to use it, it helps if it can avoid congestion.
    *Maybe in suburban Atlanta. Also, some people might not have the option of working more if they can save time spent commuting because they aren't able to find a job opportunity that allows them to do so.
    **Except for gas and infrastructure cost, but that's probably similar to the cost of a transit pass.

  2. Higher ridership means more boardings. Buses do not stop at bus stops if there is no one waiting to board or wanting to get out. So with lower ridership, a bus may stop at only 1 stop in 3 or 4, meaning an effective stop spacing of 800-1 000 meters even if there is a bus stop every 200 meters. With higher riderships, theoretically, you could just put enough buses so that the number of boardings per individual buses be the same as for the lower ridership routes, but that supposes that passengers arrive predictably at bus stops rather than randomly. The reality is that when you try to compensate by putting more buses on a route, you will get bus bunching as some buses randomly get more passengers and thus have to stop more often, slowing down, thus increasing the chance to have even more passengers in front of it. It does mean that you will likely get a faster bus behind, I've even seen nearly empty buses pass full buses on certain routes. The empty bus is faster... but it IS empty, so only few can benefit from it. Meanwhile, the bus that is full has a lot of riders hating the uncomfortable, crawling transit experience they're having.

    That means that suburban buses, since they have low ridership generally, can have short stop spacing because since buses will bypass 70-90% of them anyway, their speed will be unaffected by how close the stops are. The only thing we would achieve by increasing stop spacing is reducing even more bus use, as walking 200 or 300 meters in a suburb is often less comfortable and worse than walking the same distance in an urban area.

    There is a trade off between longer walking distances and speed with stop spacing, yet you must consider that if one follows schedules, the greater walking distance may be compensated by an earlier departure from the point of origin. So instead of waiting 2 minutes, people may be walking 2 minutes instead.

    There is a monetary argument to use the bus (thanks largely to subsidies, as most buses are subsidized at a rate of 60 to 80% in North America since ridership is so low). Still, it's important to point out that for people who have cars anyway, the marginal cost of using it is often not much higher than the cost to take the bus. Furthermore, offering a monetary advantage and not caring about poor speed and efficiency is sending mixed messages. You reward people for taking the bus by making it cheaper, then punish them for taking it by making their trips longer.

    Transit does take less space than cars (but buses take more space than pedestrians, and about as much as cyclists). However, we must distinguish between what's preferable for society and what's preferable for individuals. The problem is one of individual incentives. Taking a bus may have less externalities, people take less space, require less parking, cause less congestion, etc... but reducing externalities by definition means advantaging OTHER people. If you want to get people to take the bus, you need to explain to them why THEY THEMSELVES are advantaged by taking it. It's nice to know you're helping others, but if you waste 1 hour more a day by doing it, you feel like you're taking one for the team, and it contributes to keeping transit use way down.

    To increase transit use and offer viable alternatives, we must care about how fast transit gets people to where they want to go in comparison to other modes of transport, and to work at reducing the gap between transit and cars.

    1. I have a larger point to makeabout buses eventually, but I just wanted to say that your observation about "walking 200 or 300 meters in a suburb is often less comfortable and worse than walking the same distance in an urban area" is really spot on. And it's one of the most annoying thing about suburbs: not only are the distances much larger, but the distance one is willing to walk is shorter due to the unpleasantness of the walk (though that depends a lot on the suburb!)

  3. We have had a bad experience with wider-spaced stops in Austin. They recently replaced most of the frequency of our flagship local route the #1 and all of its express cousin the #101 with a new "premium service" 801 that includes wider stop spacing, articulated buses, rear-door entrances for those with passes (including individual ride passes purchased on smartphones), and various other advertised features.

    Since introduction, ridership on the local + premium is down 11% compared to the old local + express combination. It is hard to disentangle the effects of the price raises on the premium vs. the effects of the stop spacing, but anecdotally, the sparse stop spacing is discouraging people from taking it because of the long walk in the heat combined with the a still slow-running mixed-traffic bus. Perhaps if the buses had dedicated lanes (or traffic wasn't as bad as it is), the walk to the stops would be more tolerable.

    1. That's an interesting case study. From what I read, the 101 already had the limited stops of the 801 (or maybe a bit more?), but when they came up with the 801, they cut the frequency on the 1 line and charge people more for the 801, which has bigger buses, wifi and a lot of amenities. However, fares are 50% higher on the 801 (but still quite low by Canadian standards, 1,50$ for a bus ride? Try 3,00$ in Montréal). From what I have read, it seems they built the 801 to favor white middle-class riders with stop locations and higher fares, while cutting the capacity of the local 1 line that was used by minorities and poor people. Plus, the 801 is not faster than the 101 it replaced if I understand correctly.

      So yeah, if they cut the capacity of the existing lines and added a premium service that is 50% more expensive yet not better than the express line it replaces, it's understandable that ridership fell.

      Personally, all this stuff about wifi and special amenities in buses is quite irrelevant, it's the kind of thing people who wouldn't be caught dead in a bus answer in surveys about what could interest them in taking transit. As a bus rider (by choice), wifi is pretty irrelevant to me, especially in loaded buses where it's hard to get your phone out. What I care about is frequency, speed, punctuality (but not at the sacrifice of speed and frequency) and comfort, in that order.

      Personally, the limited stop buses I support are more like the now defunct 101 line. Regular buses (or articulated ones if there is a need for them), priced just like regular buses but with limited stops, ideally in urban areas where walking is comfortable. From checking out on Google Maps, Lamar Boulevard with narrow sidewalks frequently stuck between a 4- or 6-lane street and parking lots on the other side, wouldn't quite qualify as a street where walking is comfortable and pleasant.