Friday, October 26, 2012

Unbunching the bus, part 2

Last time I discussed some of the reasons that buses bunch. Here's some possible ways to help alleviate the problem, if put into practice:

Fewer, higher quality bus stops, with curb extensions

Bus stop consolidation or elimination is an important step: it reduces the fixed costs associated with stopping the bus. One problem is political: people are often attached to their particular stop even if another one is close-by. But American standards for bus stop spacing are too small by far. Here in Boston there's plenty of examples of buses that stop every block or two, which is self-defeating. I believe the station spacing should be closer to a quarter-mile, and not less than 800 ft.
Waldo Terrace stop in Brighton Center: barely 30 feet long!

The other problem with bus stop consolidation is the higher strain placed on the remaining ones. This can be accommodated by using money saved to improve those stops to handle the increased load. There are many cases in the city where this could be applied. For example, take Waldo Terrace in Brighton Center. The following two stops are each separated by a mere 350 feet. Waldo Terrace stop itself is only 30 feet long at best, which is far below the MBTA standards of 60 feet for a corner stop. There is no physical way for a 40 foot bus to pull into this stop when cars are parked adjacent to it. So in my experience, the drivers simply stop in the travel lane.

Stopping in the travel lane has the benefit of eliminating clearance times from the delay equation. The problem is access: the curb is too far for level boarding of any kind, and stepping up into the bus does increase dwell time. The answer is to consolidate this stop with the other two, and to build a "curb extension" or "bulb-out" at the chosen site.

Curb extension: before and after (source: TRB Bus Transit Capacity manual)

The curb extension offers a place for passengers to comfortably wait, it brings level boarding to the side of the bus, helps disabled passengers, eliminates clearance times, and it even frees up some curbside parking space. The cost is a small delay to vehicles behind the bus. But the way I see it: that delay is already happening because of the poorly designed existing stations, and it doesn't really cause a problem. Also, the curb extension (with level boarding) can greatly speed up bus boarding time, making it less of an issue. And, the transportation planner should be thinking of delay in terms of person-minutes, not vehicle-minutes. The bus, with its capacity of 50-80 people, should weigh much more heavily in the mind than the typical private automobile, with its average of one or two people per car.

Bus lanes and signal priority

On wider roads, one potential improvement is a dedicated bus lane, which eases a great deal of the variability that makes scheduling buses a headache. They would still require grade crossings at intersections, so a bus detector could be employed to shift the priority of the traffic signal on approach. Bus lanes go well with curb extensions and also eliminate the one downside of curb extensions because there shouldn't be any other vehicles waiting behind the bus. Bus lanes can also provide an outlet for emergency vehicles that are stuck in traffic jams.

Better boarding and fare payment

Going along with those improvements to bus stops should be choices made to optimize boarding and alighting times. That means purchasing vehicles with low floors, wider doorways, and using all-doors boarding -- which most likely implies deploying Proof-of-Payment and possibly pre-payment of fares. A whole other post could be written about this, so I'll leave it aside. Designs made in accordance with the Americans with Disabilities Act (and the Mass. AAB) are also generally good for improving boarding and alighting times and therefore are good for transit service.

Self-stabilizing headways

A while back, Bartholdi and Eisenstein authored a paper named "A self-coördinating bus route to resist bus bunching" (summarized here). They described a fairly simple technique for bus dispatching which can be shown mathematically to reinforce stable, equal, and naturally-arising headways as buses circulate along a route. The gist is that it works by delaying buses at strategically chosen "control points" which are stops along the route designated for special treatment. The most natural choices for control points are the termini of a bus route, where the bus must layover anyway while the driver changes or takes a break. There could be other control points as well. I noticed that VTA designed layovers at intermediate stops along its longer routes, for example (whether they made good decisions on this is another matter).

The Bartholdi and Eisenstein idea is easy to implement: the amount of delay that a bus should undertake at a control point is equal to the backwards-headway times some adjustable factor (which be a fraction between 0 and 1). That factor (called α) must be determined through empirical observations and agency policy. But the backwards-headway is easy to measure, especially these days with GPS transponders installed in every bus. Just check how far away the next bus is from arriving at the current stop, and figure out how many minutes that is, and you've got the backwards-headway.

The neat thing is that you can show, mathematically, that by using this technique, headways stabilize naturally towards equal spreading of the buses. You don't even have to know the headways in advance -- the system will naturally tend towards the ideal spacing. They implemented it for a few experiments which seem to bear out their findings. The main failing, as far as I can see it from playing with the model, is that it may take too much time to unbunch buses if there are not enough control points. The other "problem" is that it is incompatible with scheduled arrivals by nature, although for a frequent bus route the schedule is usually wrong anyhow.


  1. Drivers in Boston in general and Brighton in particular also have the annoying habit of parking in bus stops.

    1. Indeed. And in those cases, the bus is forced to stop in the street as if there was a curb extension. I would say that this is another good argument to build the curb extensions -- so that people with disabilities can still use the bus despite the selfish behavior of private vehicle drivers.

  2. That bus-unbunching algorithm seems ideal for headway-based services like the VTA's 522 Rapid, which nominally has timepoints but is allowed to leave them early. And as far as control points go, the best place to delay would be at transfer points, where delays could aid in coordinating connections and allowing two-way transfers. Plus, it seems like riders would be a bit less likely to be annoyed by waiting on a bus if they can see that the bus was waiting for a bunch of people who connected from another bus.

    1. Yes, though the 522 has a somewhat crummy 15 minute headway, IIRC. I've noticed the T often behaves similarly though: I'm finding trains and buses arriving at stops ahead of schedule when traffic is light. Especially late at night or early in the morning. In fact, I typically adjust my expectation of NextBus's reliability based on that. For example, I took the first bus of the morning one day this past week, and it was clearly moving along at a much more rapid pace than typical. A trip which took me 30 minutes during rush hour was only 15 minutes. The NextBus indicator counts minutes down much more quickly in such cases.

      I have been thinking about a few ways to do a "dynamic" timed transfer on-the-fly, but ultimately elided them from the article because I'm not sure about the effectiveness. But with computers and communications being so advanced these days, there must be something that can be done that is an improvement from 20th century-style operations.