More on Buses

In my first Report Report Report (please nominate articles for subsequent ones!) I went into some detail about the views of Austan Goolsbee and David Reiley on the subject of incentive pay for bus drivers. Both of them agree that paying bus drivers per passenger decreases wait times, but at a cost: those drivers get into many more accidents.

Both would like to see bus systems experiment with introducing incentive pay, along with safeguards which would seek to protect passengers' (and drivers') safety. Goolsbee proposes docking bonuses when a driver gets into an accident, while Reiley proposes GPS-equipped buses which calculate the average spacing between one bus and the buses in front of it and behind it.

I suspect that neither scheme would work, and that there is actually a causal relationship between shorter wait times and more accidents. If you keep everything else constant – the amount of congestion, the number of buses, the price of the fares – then any attempt to incentivise bus drivers to minimise wait times will also end up increasing the amount of accidents they get into.

To understand why, one first has to understand the reason why buses "bunch" in the first place – the well-known phenomenon whereby you wait half an hour for a bus and then three arrive at the same time. This has been understood since 1964, when it was explained in a paper by GF Newell and RB Potts. Here's Reiley, summing up:

Buses may start out with even intervals, but a small random shock, such as local traffic congestion or the arrival of a sudden influx of more passengers, causes one bus (say Bus A) to be stopped longer than usual at a stop. This may cause the bus to fall behind schedule. As it falls behind schedule, more and more passengers arrive at stops to wait for its arrival, which slows it down even more. The driver must spend extra time boarding those passengers and collecting their fares and later unboarding them. Meanwhile, Bus B, immediately following A on the same route, starts collecting fewer passengers than usual because the interval between A and B has diminished. The small initial change thus gets amplified, as Bus A makes longer and longer stops to pick up and drop off more passengers, while Bus B similarly makes shorter and shorter stops. This process continues until Bus B completely catches up to Bus A.

Now observe what happens in Santiago, where bus drivers are paid on a per-passenger basis:

Initially we conjectured that drivers would improve their spacing by slowing down if they got too close to the bus immediately ahead, but this turned out to be incorrect. In fact, once they get sufficiently close, they attempt to pass the bus in front. This ameliorates the problem of bus bunching: an empty bus proceeds more quickly (making quicker stops) than a bus full of passengers, so putting the empty bus in front of the full bus tends to reduce bunching. However, this technique often involves aggressive driving by the driver attempting to pass, which can result in an uncomfortable passenger ride or an increased probability of accidents.

There's a small irony here: in order to ameliorate bus bunching, one has to accelerate the process which causes it. Santiago has less bus bunching than other cities not because buses catch up to the bus in front less frequently, but because they catch up to the bus in front more frequently.

So now consider Reiley's proposed scheme:

With a full implementation of GPS technology, drivers could have information on the location of other buses at all times. Drivers could have a real-time display showing the locations of other buses both in front of and behind them, enabling them to respond with adjustments to the spacing. GPS technology opens up a whole new realm of contractual possibilities. For example, one might pay drivers a bonus based on the continuous-time average spacing between their bus and other buses on the route, thus providing drivers with appropriate incentives to minimize passenger waiting time.

Under this scheme, what is a bus driver to do if he finds himself gaining on the bus in front? He basically has two choices: either slow down or speed up. Given his incentives, the obvious move would be to slow down, since that would increase the spacing between himself and the bus in front, and thereby increase his bonus. But the bus in front is only going to get slower and more crowded so long as it doesn't have a bus in front helping to pick up the extra passengers who are accumulating and waiting for it. So wait times will go up, not down. What's more, one overcrowded slow bus could end up slowing down a whole convoy of buses behind it – meaning not only longer wait times, but longer travel times as well.

But what happens if the second bus decides to speed up, and overtake the bus in front? That would decrease wait times, but might well have an adverse effect on the driver's bonus. For all the time that the second bus is decreasing the gap between himself and the bus in front, he is also decreasing his bonus. And then once he's overtaken the bus in front, he'll be picking up large amounts of passengers who have been waiting a long time, so it's going to be more difficult for him to pull away from the bus behind and start increasing his bonus. In order to maximise pay, he would have to exhibit the tendencies seen in Santiago: leaving the bus stop before everybody has fully boarded, and maybe even missing bus stops in order to get some space between himself and the bus behind him. All of which is dangerous behaviour which shouldn't be incentivised.

How about a slightly different incentive system? Austan Goolsbee emailed me:

The best way to address such problems is to give incentives that include more than just one criteria. You could pay the drivers by the passenger but penalize them for accidents, for example.

I'm not sure that would work either. In Santiago, the incentivised drivers have 10 accidents for every million kilometers they drive. If they drive 100km per day, that means they have one accident every 1,000 days: on average they will go three years without an accident, even driving as dangerously as they do. In order to make the drivers drive more safely, the penalties would have to be huge. That would have two effects: it would unfairly penalize drivers who got into an accident through absolutely no fault of their own, and it would give drivers a very strong incentive not to report any but the most serious accidents.

The real, underlying problem is that it's far from obvious exactly what behaviour one wants to incentivise. In Santiago, there's a clear and strong correlation between how fast a bus driver drives and how much he gets paid. Or, to put it another way, there's a strong correlation between how aggressively drivers drive and how much average wait times are cut. More aggression means shorter waits. So do cities want to reward aggression in their bus drivers? You can't have it both ways: tell bus drivers that you want them to cut average wait times, but at the same time tell them that you don't want them to be more aggressive. The two work against each other, and you'll end up with sheer confusion.

It seems to me that the easiest ways of decreasing wait times are the most obvious: increase the number of buses, increase the number of bus lanes, decrease the amount of congestion. Pace Goolsbee's original article in Slate, drivers in Chicago could also simply be given permission to take surface streets when Lake Shore Drive is backed up. Incentive pay is an interesting idea, but I'm far from convinced it can work well in practice.

Posted by Felix at 12:15 EST