Why do three buses always come along at once? This game explains

Typical. Bloody typical. Two London buses serving the same route, bunched up in the Clapton area. Image: Felix O, via Flickr.

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.


What does the fate of Detroit tell us about the future of Silicon Valley?

Detroit, 2008. Image: Getty.

There was a time when California’s Santa Clara Valley, bucolic home to orchards and vineyards, was known as “the valley of heart’s delight”. The same area was later dubbed “Silicon Valley,” shorthand for the high-tech combination of creativity, capital and California cool. However, a backlash is now well underway – even from the loyal gadget-reviewing press. Silicon Valley increasingly conjures something very different: exploitation, excess, and elitist detachment.

Today there are 23 active Superfund toxic waste cleanup sites in Santa Clara County, California. Its culture is equally unhealthy: Think of the Gamergate misogynist harassment campaigns, the entitled “tech bros” and rampant sexism and racism in Silicon Valley firms. These same companies demean the online public with privacy breaches and unauthorised sharing of users’ data. Thanks to the companies’ influences, it’s extremely expensive to live in the area. And transportation is so clogged that there are special buses bringing tech-sector workers to and from their jobs. Some critics even perceive threats to democracy itself.

In a word, Silicon Valley has become toxic.

Silicon Valley’s rise is well documented, but the backlash against its distinctive culture and unscrupulous corporations hints at an imminent twist in its fate. As historians of technology and industry, we find it helpful to step back from the breathless champions and critics of Silicon Valley and think about the long term. The rise and fall of another American economic powerhouse – Detroit – can help explain how regional reputations change over time.

The rise and fall of Detroit

The city of Detroit became a famous node of industrial capitalism thanks to the pioneers of the automotive age. Men such as Henry Ford, Horace and John Dodge, and William Durant cultivated Detroit’s image as a centre of technical novelty in the early 20th century.

The very name “Detroit” soon became a metonym for the industrial might of the American automotive industry and the source of American military power. General Motors president Charles E. Wilson’s remark that, “For years I thought what was good for our country was good for General Motors, and vice versa,” was an arrogant but accurate account of Detroit’s place at the heart of American prosperity and global leadership.

The public’s view changed after the 1950s. The auto industry’s leading firms slid into bloated bureaucratic rigidity and lost ground to foreign competitors. By the 1980s, Detroit was the image of blown-out, depopulated post-industrialism.

In retrospect – and perhaps as a cautionary tale for Silicon Valley – the moral decline of Detroit’s elite was evident long before its economic decline. Henry Ford became famous in the pre-war era for the cars and trucks that carried his name, but he was also an anti-Semite, proto-fascist and notorious enemy of organised labor. Detroit also was the source of defective and deadly products that Ralph Nader criticized in 1965 as “unsafe at any speed”. Residents of the region now bear the costs of its amoral industrial past, beset with high unemployment and poisonous drinking water.

A new chapter for Silicon Valley

If the story of Detroit can be simplified as industrial prowess and national prestige, followed by moral and economic decay, what does that say about Silicon Valley? The term “Silicon Valley” first appeared in print in the early 1970s and gained widespread use throughout the decade. It combined both place and activity. The Santa Clara Valley, a relatively small area south of the San Francisco Bay, home to San Jose and a few other small cities, was the base for a computing revolution based on silicon chips. Companies and workers flocked to the Bay Area, seeking a pleasant climate, beautiful surroundings and affordable land.

By the 1980s, venture capitalists and companies in the Valley had mastered the silicon arts and were getting filthy, stinking rich. This was when “Silicon Valley” became shorthand for an industrial cluster where universities, entrepreneurs and capital markets fuelled technology-based economic development. Journalists fawned over successful companies like Intel, Cisco and Google, and analysts filled shelves with books and reports about how other regions could become the “next Silicon Valley”.

Many concluded that its culture set it apart. Boosters and publications like Wired magazine celebrated the combination of the Bay Area hippie legacy with the libertarian individualism embodied by the late Grateful Dead lyricist John Perry Barlow. The libertarian myth masked some crucial elements of Silicon Valley’s success – especially public funds dispersed through the U.S. Defense Department and Stanford University.

The ConversationIn retrospect, perhaps that ever-expanding gap between Californian dreams and American realities led to the undoing of Silicon Valley. Its detachment from the lives and concerns of ordinary Americans can be seen today in the unhinged Twitter rants of automaker Elon Musk, the extreme politics of PayPal co-founder Peter Thiel, and the fatuous dreams of immortality of Google’s vitamin-popping director of engineering, Ray Kurzweil. Silicon Valley’s moral decline has never been clearer, and it now struggles to survive the toxic mess it has created.

Andrew L. Russell, Dean, College of Arts & Sciences; Professor of History, SUNY Polytechnic Institute and Lee Vinsel, Assistant Professor of Science and Technology Studies, Virginia Tech.

This article was originally published on The Conversation. Read the original article.