Q: Why do buses come in threes? A: Mathematical inevitability

That's the problem with the internet in summer, isn't it? Nothing but repeats. 

Anyway, here's something we originally published in June 2015. But it's dead good, honest.

The old joke that you wait ages for one bus, then three come along at once, is bordering on cliché. But it's also, as it turns out, true – not just because of bad planning, but also because of maths.

The phenomenon is so common, in fact, that it has a choice of names. Bus bunching, clumping, convoying, platooning – all relate to the depressing reality that, over any length of time, buses serving a single route are likely to end up tootling along directly behind each other.

The reasons why this should be can be difficult to get your head around – so Lewis Lehe, a postgrad working on a PhD in transport engineering at the University of California, Berkeley, has built a game of sorts to demonstrate. You can play it here. But if, like us, you are both lazy and impatient, here's how it works, with a few helpful screenshots to illustrate. 

The game features two buses, serving a circular route with four stops. At the start of the game, the two buses are evenly spaced, at opposing ends of the loop. Passenger flows at each stop are identical to those opposite: when one bus has to pause for a set period at one stop, the other is pausing for the same length of time across the map.

The result is that the two buses are always carrying the same number of passengers. Left to their own devices, they will remain equally spaced forever, in perfect equilibrium.

And we know this, because at this point we got distracted, had a conversation on Twitter, went to make a coffee, and then suddenly remembered we were in the middle of doing something about buses, flicked back to the game in a panic, and discovered that it looked like this:

Our game was still ticking along nicely, the two buses now holding seven passengers apiece.

Eternal equilibrium is really boring, though, so let's mess things up a bit. What happens if we delay Bus One, just for a single second?

Err, well, this as it turns out. This is a couple of moments after the unexpected delay.

Two things to notice here. One is that the gap between the two buses has closed, slightly: that momentary delay allowed Bus Two to catch up, slightly. The other thing is that Bus One now has more passengers.

Those two things are actually features of a single phenomenon. In those few moments in which Bus One was delayed, Bus Two started to catch up – not by much, but for enough for it to have an effect. The consequence is that it's now reaching stops which last saw a bus relatively recently – and where there are fewer passengers for it to pick up.

But here's the insidious thing: that process is self-perpetuating.

Think this through for a moment. If Bus Two is serving stops that have relatively fewer passengers waiting, it can get moving again faster. Bus One, by contrast, is serving stops that haven't seen a bus in a while (it was delayed, after all), and so it's picking up more people. That means it needs to stop for longer, both to let its larger contingent of people off, and to collect the next lot.

And so, Bus Two gets closer...

...and then catches up altogether.

 

Look at the distribution of passengers now. Bus One is now arriving at stops with populations bigger than some small Chinese cities. Bus Two, just behind, arrives moment later to find them deserted. Without intervention, this situation will persist, essentially, forever.


In real life, of course, there would be an intervention (Bus Two would almost certainly overtake, as soon as there’s room). And real life is messier than this model in other ways, too. Bus routes are served by more than two buses; passenger flows aren't so evenly spread.

But it’s this inevitable messiness that provides that slight delay that kicks the whole process off. A slight disparity in passenger numbers, a traffic jam, bad luck with the lights; whatever the cause, one bus will be delayed, and those behind it will start to catch up.

Until suddenly you get three buses showing up at once and everyone makes tutting noises.

There are ways of mitigating this feedback loop. One is setting maximum or minimum stopping times in advance, to regulate the service. Another is building in waiting time at one end of a route, so that a bus doesn't immediately turn around and set off again (in effect, doing the second half of a circular route), thus bringing a measure of predictability to the time it takes to do an entire circuit.

These things can help – but the ubiquity of bus bunching suggests that they can’t elimate the problem altogether.

So the next time someone in your hearing asks why it is that buses all come along at once, you can reply, "Mathematical inevitability". Then you can look smug about it, as they, presumably, decide that they’d rather walk.

 
 
 
 

Urgently needed: Timely, more detailed standardized data on US evictions

Graffiti asking for rent forgiveness is seen on a wall on La Brea Ave amid the Covid-19 pandemic in Los Angeles, California. (Valerie Macon/AFP via Getty Images)

Last week the Eviction Lab, a team of eviction and housing policy researchers at Princeton University, released a new dashboard that provides timely, city-level US eviction data for use in monitoring eviction spikes and other trends as Covid restrictions ease. 

In 2018, Eviction Lab released the first national database of evictions in the US. The nationwide data are granular, going down to the level of a few city blocks in some places, but lagged by several years, so their use is more geared toward understanding the scope of the problem across the US, rather than making timely decisions to help city residents now. 

Eviction Lab’s new Eviction Tracking System, however, provides weekly updates on evictions by city and compares them to baseline data from past years. The researchers hope that the timeliness of this new data will allow for quicker action in the event that the US begins to see a wave of evictions once Covid eviction moratoriums are phased out.

But, due to a lack of standardization in eviction filings across the US, the Eviction Tracking System is currently available for only 11 cities, leaving many more places facing a high risk of eviction spikes out of the loop.

Each city included in the Eviction Tracking System shows rolling weekly and monthly eviction filing counts. A percent change is calculated by comparing current eviction filings to baseline eviction filings for a quick look at whether a city might be experiencing an uptick.

Timely US eviction data for a handful of cities is now available from the Eviction Lab. (Courtesy Eviction Lab)

The tracking system also provides a more detailed report on each city’s Covid eviction moratorium efforts and more granular geographic and demographic information on the city’s evictions.

Click to the above image to see a city-level eviction map, in this case for Pittsburgh. (Courtesy Eviction Lab)

As part of their Covid Resource, the Eviction Lab together with Columbia Law School professor Emily Benfer also compiled a scorecard for each US state that ranks Covid-related tenant protection measures. A total of 15 of the 50 US states plus Washington DC received a score of zero because those states provided little if any protections.

CityMetric talked with Peter Hepburn, an assistant professor at Rutgers who just finished a two-year postdoc at the Eviction Lab, and Jeff Reichman, principal at the data science research firm January Advisors, about the struggles involved in collecting and analysing eviction data across the US.

Perhaps the most notable hurdle both researchers addressed is that there’s no standardized reporting of evictions across jurisdictions. Most evictions are reported to county-level governments, however what “reporting” means differs among and even within each county. 

In Texas, evictions go through the Justice of the Peace Courts. In Virginia they’re processed by General District Courts. Judges in Milwaukee are sealing more eviction case documents that come through their courtroom. In Austin, Pittsburgh and Richmond, eviction addresses aren’t available online but ZIP codes are. In Denver you have to pay about $7 to access a single eviction filing. In Alabama*, it’s $10 per eviction filing. 

Once the filings are acquired, the next barrier is normalizing them. While some jurisdictions share reporting systems, many have different fields and formats. Some are digital, but many are images of text or handwritten documents that require optical character recognition programs and natural language processors in order to translate them into data. That, or the filings would have to be processed by hand. 

“There's not enough interns in the world to do that work,” says Hepburn.


Aggregating data from all of these sources and normalizing them requires knowledge of the nuances in each jurisdiction. “It would be nice if, for every region, we were looking for the exact same things,” says Reichman. “Instead, depending on the vendor that they use, and depending on how the data is made available, it's a puzzle for each one.”

In December of 2019, US Senators Michael Bennet of Colorado and Rob Portman of Ohio introduced a bill that would set up state and local grants aimed at reducing low-income evictions. Included in the bill is a measure to enhance data collection. Hepburn is hopeful that the bill could one day mean an easier job for those trying to analyse eviction data.

That said, Hepburn and Reichman caution against the public release of granular eviction data. 

“In a lot of cases, what this gets used for is for tenant screening services,” says Hepburn. “There are companies that go and collect these data and make them available to landlords to try to check and see if their potential tenants have been previously evicted, or even just filed against for eviction, without any sort of judgement.”

According to research by Eviction Lab principal Matthew Desmond and Tracey Shollenberger, who is now vice president of science at Harvard’s Center for Policing Equity, residents who have been evicted or even just filed against for eviction often have a much harder time finding equal-quality housing in the future. That coupled with evidence that evictions affect minority populations at disproportionate rates can lead to widening racial and economic gaps in neighborhoods.

While opening up raw data on evictions to the public would not be the best option, making timely, granular data available to researchers and government officials can improve the system’s ability to respond to potential eviction crises.

Data on current and historical evictions can help city officials spot trends in who is getting evicted and who is doing the evicting. It can help inform new housing policy and reform old housing policies that may put more vulnerable citizens at undue risk.

Hepburn says that the Eviction Lab is currently working, in part with the ACLU, on research that shows the extent to which Black renters are disproportionately affected by the eviction crisis.

More broadly, says Hepburn, better data can help provide some oversight for a system which is largely unregulated.

“It's the Wild West, right? There's no right to representation. Defendants have no right to counsel. They're on their own here,” says Hepburn. “I mean, this is people losing their homes, and they're being processed in bulk very quickly by the system that has very little oversight, and that we know very little about.”

A 2018 report by the Philadelphia Mayor’s Taskforce on Eviction Prevention and Response found that of Philadelphia’s 22,500 eviction cases in 2016, tenants had legal representation in only 9% of them.

Included in Hepburn’s eviction data wishlist is an additional ask, something that is rarely included in any of the filings that the Eviction Lab and January Advisors have been poring over for years. He wants to know the relationship between money owed and monthly rent.

“At the individual level, if you were found to owe $1,500, was that on an apartment that's $1,500 a month? Or was it an apartment that's $500 a month? Because that makes a big difference in the story you're telling about the nature of the crisis, right? If you're letting somebody get three months behind that's different than evicting them immediately once they fall behind,” Hepburn says.

Now that the Eviction Tracking System has been out for a week, Hepburn says one of the next steps is to start reaching out to state and local governments to see if they can garner interest in the project. While he’s not ready to name any names just yet, he says that they’re already involved in talks with some interested parties.

*Correction: This story initially misidentified a jurisdiction that charges $10 to access an eviction filing. It is the state of Alabama, not the city of Atlanta. Also, at the time of publication, Peter Hepburn was an assistant professor at Rutgers, not an associate professor.

Alexandra Kanik is a data reporter at CityMetric.