# ‘Slower’ passengers such as having children with children first go on board is really faster

Research into ‘slower’ passengers such as having children with children first board aircraft is really faster than boarding back-to-front, randomly or quickly first.

Norway-led researchers used space-time geometry techniques to investigate the factors that lead to a fast start or a painful slowdown on the asphalt.

They calculated the boarding times based on the passenger chains that are in each other’s way while they try to settle in their seats.

The more passengers can sit down at the same time – the so-called ‘parallelism’ – the less congestion builds up and the faster boarding can proceed.

Slower passengers need more time to put their luggage away and sit down – so having faster starts boarding as the slower settlement increases the parallelism.

This in turn speeds up the overall boarding process and reduces the risk of delayed departure times that could have a knock-on effect on the global network of air travel.

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‘Slower’ passengers such as having children with children first go on board is really faster than boarding back-to-front, randomly or quickly first, a study has shown

Statistician Sveinung Erland from the University of West Norway and colleagues decided to tackle the problem of boarding aircraft with the help of the so-called ‘Lorentzian geometry’.

This space-time geometry is the same branch of mathematics that underlies Albert Einstein’s famous general theory of relativity.

The team considered the well-known relationship between the microscopic dynamics of a series of interacting particles and the corresponding properties on a wider scale – a relationship that is an important theme in statistical physics.

Or, translated in the context of the boarding process, they considered the relationship between the interaction of boarding passengers in a row and the overarching time that everyone needs to sit.

“The ability of a passenger to postpone other passengers depends on their queue positions and driving indications,” the team wrote in their paper.

“This is similar to the causal relationship between two events in space time, while two passengers are time bound if one blocks the other and the space as if both can sit at the same time.”

In their model, the researchers considered boarding a two-part process, in which the passengers took a one-dimensional line down the aisle and eventually settled in a matrix of seats.

Norway-led researchers used space-time techniques to investigate the factors that lead to a fast start or a painful delay on the asphalt

First, passengers go through the aisle until they reach their assigned row or are temporarily blocked by other travelers in front of them.

After each passenger has reached his line, the model then considered how long he would have to stand in the aisle to store his hand luggage in an upper compartment and then sit down.

By combining these steps, the model could determine whether individual passengers would eventually block each other based on their relative positions in the queue and how far they are from their seat assignments.

In general, the time required to place the entire passenger compartment depends on where each row is located, to which row they are traveling and how long it takes for them to store and sit down their luggage.

They calculated the boarding times based on the passenger chains that are in each other’s way while they try to settle in their seats. The more passengers can sit down at the same time, the less congestion accumulates and the faster boarding can proceed

The researchers discovered that the line to take passengers on board can be represented as a series of waves – where each wave represents groups of passengers who can all sit down at the same time.

“That is why the boarding time is the product of the aisle time of the aisle times the number of wave fronts needed to transport all passengers,” the researchers explained.

To calculate this quickly, the model uses so-called ‘blocking chains’ – series of passengers who in turn block each other and are equivalent to the causal chains of events in space-time geometry.

The longest blocking chain during boarding determines the total boarding time – which in turn will be equal to the sum of the transit times of each passenger in the chain.

Starting with one of the passengers who will sit last and work forward – taking into account the closest traveler in the line who can block the current one until a passenger in the first wave is reached – the longest chain length can be found.

In general, the time it takes to place the entire passenger compartment depends on where each row is located, which row they go to and how long it takes for them to put their luggage away and sit down

With this approach, the researchers were able to test different entry strategies that airlines could use – from getting slower passengers up to randomly boarding.

They came up with the apparently counter-initiative and found that it is about 28 percent more efficient to let the slower passengers first board a plane compared to the faster passengers first boarding.

“This is a universal result, valid for any combination of parameters that characterize the problem,” the team wrote.

Such parameters included “the percentage of slow passengers, the ratio between transit times of the fast and slow group and the density of passengers along the aisle.”

With this approach, the researchers were able to test different entry strategies that airlines could use – from getting slower passengers up to randomly boarding. They found that it is about 28 percent more efficient to let the slower passengers first board an aircraft compared to the faster passengers first boarding

The findings are similar to a similar study conducted by the American physicist Jason Steffen in 2011.

Professor Steffen approached the problem differently, using a so-called “Markov chain Monte Carlo” algorithm that used random changes to find iteratively the best solution for a given scenario.

He concluded from this that the best approach – called the ‘Steffen method’ – uses boarding in waves where adjacent seated passengers are separated from each other in the embarkation line, thereby minimizing crowding in the aisle of the aircraft.

Field tests have shown the success of this strategy, which is twice as fast as back-to-front boarding (as most airlines currently do) and 20-30 percent faster than random boarding.

The key to both the Steffen method and the findings of Professor Erland and colleagues is that boarding is faster when more passengers can take a seat at the same time – a principle that Professor Steffen calls ‘parallelism’.

“The parallel you can make the entry process, the faster it will go,” he said Ars Technica.

“It’s not so much about structuring things, but about finding the best way to let several people sit down at the same time.”

In the slowest boards-first strategy followed by the recent study, parallelism is achieved because the first of the faster passengers can take their seats while the last of the slower passengers is still sitting.

On the other hand, if the faster passengers board first, the fast passengers can sit down before the first of the slow passengers can follow the example – which reduces the parallelism of the boarding.

“That is the lesson of this [latest] result, “Professor Steffen told Ars Technica.

‘If you want to put a number of passengers in a ship like this, and you divide them into slow people versus fast people, it is better to first get rid of the slow people and then let the fast people trickle in. “

In reality, there are composite factors that really make boarding more complex – such as competition for limited luggage space, troublesome passengers, cabin crew movement and preferably first-class boarding passengers.

Nevertheless, such studies are still useful starting points, Professor Steffen insisted.

“It gives you measurable results to consider when drawing up policies,” he told Ars Technica.

“And it is counter-intuitive information that makes it even more valuable because it shows where your intuition can lead you astray.”

The full findings of the study were published in the journal Physical assessment E.

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