Letting ‘slower’ passengers like those with children board aeroplanes first really is faster than boarding the back rows first, randomly or fastest first, a study has found.

A team of researchers led from Norway used space-time geometry techniques to explore the factors that lead to a speedy take-off or an agonising delay on the tarmac.

They calculated boarding times based on the chains of passengers that get in each others way as they try to settle in their seats.

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

Slower passengers need more time to stow their luggage and sit down — so having faster ones begin to board as the slower ones finish settling increases parallelism.

This, in turn, speeds up the overall boarding process and reduces the risk of delayed departures that can have a knock-on effect across the global air travel network.

Statistician Sveinung Erland of the Western Norway University of Applied Sciences and colleagues decided to tackle the aircraft boarding problem using so-called ‘Lorentzian geometry’.

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

The team considered the known connection between the microscopic dynamics of a set of interacting particles and the corresponding broader-scale properties — a relationship which is a key theme in statistical physics.

Or, translated into the context of the boarding process, they considered the relationship between the interaction of embarking passengers in a line and the overarching time that it will take for everyone to be seated.

‘The ability of a passenger to delay other passengers depends on their queue positions and row designations,’ the team wrote in their paper.

‘This is equivalent to the causal relationship between two events in space-time.’

In their model, the researchers treated boarding as a two-part process, with the passengers occupying a one-dimensional line down the aisle and ultimately settling into a matrix of seats.

Firstly, passengers move down the aisle until either they reach their assigned row, or are temporarily blocked by other travellers in front of them.

Once each passenger has reached their row, the model next considers how long they will need to stand in the aisle to stow their hand luggage in an overhead compartment and then sit down.

Putting these steps together, the model can determine whether individual passengers will end up blocking each other based on their relative positions in line and how far apart their seat allocations are.

Overall, the time it takes for the full passenger complement to be seated depends on exactly where in line each is located, which row they are heading for, and how long it takes each to stow their luggage and sit down.

The researchers found that the queue of embarking passengers can be imagined as a series of waves — with each wave representing groups of passengers that can all take their seats at the same time.

‘Hence, the boarding time is the product of the aisle clearing time times the number of wave fronts needed to seat all passengers,’ the researchers explained.

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

The longest blocking chain during embarkation will determine the overall boarding time — which in turn will equal the sum of the aisle-clearing times of each passenger in the chain.

Starting from one of the passengers that will be seated last and working forward — considering in turn the nearest traveller in the queue that can block the current one until reaching a passenger in the first wave — the longest chain length can be found.

With this approach, the researchers were able to test various boarding strategies airlines might employ — from letting slower passengers embark first to boarding in random orders.

They came to the seemingly counter-initiative finding that it is around 28 per cent more efficient to let the slower passengers board an aircraft first in comparison with letting the faster ones embark first.

‘This is a universal result, valid for any combination of the parameters that characterise the problem,’ the team wrote.

Such parameters included ‘the percentage of slow passengers, the ratio between aisle-clearing times of the fast and the slow group, and the density of passengers along the aisle.’

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

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

From this, he concluded that the best approach — dubbed ‘the Steffen method’ — uses boarding in waves where adjacent-seated passengers are separated from each other in the embarkation line, minimising crowding in the plane’s aisle.

Field tests demonstrated the success of this strategy, which is twice as fast as boarding back-to-front (as most airlines do at present) and 20–30 per cent faster than random boarding.

The key to both the Steffen method and the findings of Professor Erland and colleagues is that boarding occurs faster when more passengers can take their seats simultaneously — a principle Professor Steffen refers to as ‘parallelism’.

‘The more parallel you can make the boarding process, the faster it will go,’ he told Ars Technica.

‘It’s not about structuring things as much as it is about finding the best way to facilitate multiple people sitting down at the same time.’

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

In contrast, letting the faster passengers board first can result in the fast passengers already being seated before the first of the slow passengers can follow suit — reducing the parallelism of the boarding.

‘That’s the lesson of this [latest]result,’ Professor Steffen told Ars Technica.

‘If you’re going to pour a bunch of passengers into a vessel like this, and you’re dividing them up into slow people versus fast people, it’s better to get the slow people out of the way first and then let the fast people trickle in.’

In reality, there are compounding factors that make real boarding more complex — such as competition for limited overhead luggage space, difficult passengers, the movement of the cabin crew and preferentially boarding first class travellers.

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

‘It gives you a quantifiable result to consider when crafting policy,’ he told Ars Technica.

‘And it’s counter-intuitive information, which 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 Review E.