Headway based scheduling

Note: In 2012, BEST was what I called headway based scheduling before I knew that it had an accepted name.

-----Original Message-----
From: Russ Tilleman [mailto:russ.tilleman@gmail. com]
Sent: Wednesday, January 25, 2012 7:23 PM
To: Stephen Newhouse
Subject: Bus Bunching and BEST scheduling

Hi Steven,

I enjoyed talking with you this afternoon about bus scheduling. Here is a description of the BEST (Buses at Evenly Spaced Times) approach as our group has been considering it and factoring in what you and I discussed today.

Our understanding is that once a bus falls behind by a small amount, it continues to fall further behind. This is because a bus that is running 17 minutes behind the one in front of it will have to pick up more riders than a bus that is running only 15 minutes behind the one in front. Because there is 2 more minutes of time for additional riders to accumulate at the bus stops.

Conversely, when a bus is running 2 minutes behind schedule, the following bus will speed up, because there is only 13 minutes of time for riders to accumulate at the stops after the first bus is there. So the first bus slows down as the second bus speeds up. The further behind schedule the first bus gets, the more it slows down and the more the second bus speeds up. Eventually, the second bus catches up to the first one. Its a dynamically unstable system, so even small offsets in the timing of any bus can set off a cascading collapse of the schedule.

Ideally, we would like to speed up the first bus, to keep it on schedule, but this is not always practical. There are reasons it is running behind, and we can't really do much about them. However, we can do the next best thing, and keep the buses spaced on 15 minute intervals.
Each one might be a little behind schedule, but riders would be assured that they would never have to wait more than approximately 15 minutes for a bus to arrive.

Keeping the buses evenly spaced can improve service for riders without adding additional buses, or it can cut costs for AC Transit by reducing the number of buses and providing the current quality of service. Or a combination of the two. Having an empty bus tailgating a full one is an inefficient use of resources.

The way to keep the buses evenly spaced is very simple in theory. All that has to be done is to tell the driver of each bus to stay at least 15 minutes behind the bus in front. When a driver is ready to leave a bus stop, if the previous bus left that stop less than 15 minutes before, that driver can wait at that stop until the 15 minutes has passed.

If done properly, this should only result in very short holding times at each stop. Maybe a few seconds or a minute. The trick is to keep the buses from getting very far off the 15 minute spacing in the first place, so that large corrections are not needed. And keeping the "second" bus 15 minutes behind the first one helps prevent the "third" bus from slowing down, because it keeps the interval between them down to 15 minutes.

There are some modified versions of this approach that might be used that might work a little better in some cases. For example, if one bus falls way behind schedule, the following buses might be spaced 10 minutes apart rather than 15 to allow them to get back on schedule. Or let buses get within 13 or 14 minutes of each other to allow a little time for minor fluctuations. The details are less important here than just the fact that there is a simple approach that should be able to largely solve the problem.

In practice, there has to be some way to tell the drivers what to do. One good possibility is to use the GPS systems on the buses, that are currently used to predict when a bus will arrive at a particular stop, to keep track of when the previous buses reached the stops. Then the GPS system could inform the driver of how long a hold was necessary at each stop. A simple counter might be displayed with a countdown: 3, 2, 1, GO. This would be very easy for the driver to interpret and might only involve a software upgrade for the GPS systems currently on the buses. Also, the green-light-priority software might choose to not request priority if the bus is ahead of its intended interval.

In addition to improving the transit experience for riders, BEST should also help preserve the break times for drivers, because there is never a rush to get back on schedule. Break time is just another interval that is preserved. Running buses based on intervals instead of a published timetable might also allow the intervals between buses to be varied slightly over the day. For example, if a large increase in ridership is expected at 5pm, the 5:15 bus might be shifted to 5:10 and the 5:30 bus might be shifted to 5:20. This might be advantageous even if it resulted in longer intervals after 5:30, like 4:30, 4:45, 5:00, 5:10, 5:20, 5:40, 6:00, 6:15. And when traffic and ridership is light, the buses can move at the shortest intervals possible, rather than being restricted to a fixed timetable.

Issues like the bus drivers being delayed at the end of their shift have to be considered, but we think BEST can provide enough improvements in efficiency to offset any negative effects.

My suggestion would be to try out BEST on one or more bus lines for a week or something like that. All that would be required would be for someone to watch the GPS information and call up the drivers and tell them to wait as necessary. It wouldn't require any software work to do that. I suspect there would be a noticeable improvement is convenience for the riders and in preservation of break time for the drivers. If BEST passes that test and demonstrates that it really can improve things, then the issue of how to get the software modified can be addressed.

Our group of activist-minded people would like to help as much as we can to get bus bunching fixed somehow. If BEST looks like something that might work for AC Transit, we can push for it to be tested and implemented by contacting our representatives and by passing the word on to more people to contact their representatives.

I have spoken with a lot of people about intervals vs. poorly-maintained-schedules and essentially everyone has expressed a preference for the shortest intervals possible. Because people's lives don't always match the AC Transit schedule, there is some amount of waiting that people would have to do even if the buses were always perfectly on schedule. If they can just go to the bus stop at any time and know that there will always be a bus in 15 minutes and they will never have to wait 30 minutes (and see 2 buses arrive at once), life would be much easier for them.

BEST also seems to work in synergy with the NextBus system, because people can adjust their plans so that they arrive at the bus stop just before the bus gets there whether the bus is on a fixed schedule or not. If buses are bunched up, NextBus can only tell them that their choices are pairs of buses that are 30 minutes apart. But with BEST, the riders will have choices that are 15 minutes apart, which is a big improvement. By allowing riders to plan for the reality of when the buses are running, NextBus removes some of the value of fixed bus schedules, resulting in an even better trade-off in favor of BEST.

Let me know what you hear back...


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