Bused up. Commuters can help keep transport moving (Image: Tony Kyriacou/Rex Features)

Anyone who has waited for a bus knows the routine: you wait far longer than you should, then three come along at once. The problem, called “platooning”, plagues buses, trains and even elevators.

Now systems complexity researchers Carlos Gershenson and Luis Pineda of the National Autonomous University of Mexico have devised a mathematical model that shows how the problem might be prevented: transport managers need to get a little meaner about boarding times, and passengers should realise that jumping on the first train or bus that arrives won’t always help them reach a destination faster.

Clumping effect

Public transport vehicles – underground trains, for example – set off from the start of their routes equally spaced. The problem starts when one is briefly delayed, making more time for passengers to accumulate at stations further down the track. Since passenger boarding is the main factor delaying trains, these extra people slow the train even more.


Meanwhile, the gap between the delayed train and the one behind is shortened. That means fewer passengers for the train behind to pick up, making it pass through stations faster until it catches the train ahead. Eventually, all the trains on a route can end up crawling after the slowest, lead train.

If vehicles can overtake, as buses or elevators can, it just means the overtaking vehicle will pick up the people who have accumulated at the next stop, and so will slow down again.

On the Mexico City metro at rush hour, for example, platooning can treble trip times. “Trains stop for long times at and between stations, even when they are not full, because full trains get delayed in front of them,” says Gershenson.

Sticking plaster

To fix the problem, transport managers tend to focus on reactive measures such as adding extra trains at peak times, tinkering with schedules and shifting passengers offtrains at the front of a jam by announcing it will skip a few stations.

But there are ways to stop platoons forming in the first place, say Pineda and Gershenson.

The pair built an “agent based” computer model, in which trains exhibit individual rather than average behaviour. They found adding more trains just led to longer platoons; and when trains could pass each other, they just shuffled their order within the platoon – one slowcoach always led.

So they attacked the heart of the problem by preventing the spacing between the virtual trains from changing. They tried making trains spend a minimum time in a station, to prevent them from speeding up. They also made trains leave after a certain maximum time to prevent slowing. Passengers were allowed to disembark, but the trains would leave the station even if boarding was not completed. When the trains had to meet both conditions, and the maximum times were extended at peak periods, platoons never formed.

Commuter cooperation

Gershenson and Pineda now want to test the system with buses on their university campus and with real trains on the Mexico City underground. Adjusting maximum waiting times to match passenger densities should be possible, says Gershenson, by using systems that can monitor passenger flow electronically, such as gate sensors.

However they warn that the measures will need to be carefully explained to passengers, who are otherwise likely to be upset when trains start leaving them on the platform.

So can the commuter help to prevent the problem? The pair’s advice chimes with what many experienced travellers already practise – if a crowded train arrives, wait for the next one. It not only makes commuting less stressful, but smoothes the system for everyone. “Passenger behaviour is the main cause” of platoons, says Gershenson.

Journal reference: PLoS One, DOI: 10.1371/journal.pone.0007292