Scientists have created a new

model fit people in the plane with the help of the mathematical apparatus of the theory

of relativity. Analysis of the obtained regularities and numerical calculations showed

the reduction in total time in the case of applying the rule “first more

slow passengers” regardless of the parameter combinations. Maximum

the benefit regarding priority boarding more agile people came to 28

percent, write the authors in the journal Physical Review E.

Many life situations

similar to consider the physics of the problem. In particular, statistical physics

studies the relationship of the microscopic dynamics of interacting particles with

macroscopic characteristics of the entire system. By that

the approach may be applied to modelling social phenomena where people are

itself rather similar, for example, are in the queue.

One of those situations

it turns out the passengers boarding the plane. In this case, the people meet

consider the physics of particles (atoms or molecules), and macroscopic

the observed temperature may be the total time to be seated. Scientists

carried out many numerical simulations of this process, airlines

used a different technique of landing, but the success of such initiatives, as a rule,

was negligible.

Today we know that in

the limit of a large number of passengers landing increases as the square

the root of the number of passengers. Moreover, in most cases quite easily

to find the optimal arrangement of passengers in the queue

guarantee the lowest landing. However, from a practical point of view

the value of such solutions is small for psychological reasons: people tend not

to follow so strict rules, but passengers travelling together

prefer to be in the group.

Scientists from Norway,

Latvia and Israel under the leadership of Sveinung of Erland (Sveinung Erland) developed

a new approach to the problem of finding optimal rules, which combines

advantages of the mathematical apparatus of the theory of relativity with the split

passengers into two groups. The authors analyzed the effectiveness of four rules

landing: “first slow”, “fast first”, without ordering and “from tail to nose.”

In this formulation, the slow could be people with children, with bulky hand baggage

requiring special assistance and other categories of passengers.

The approach description of the problem in terms of the Lorentz metric, that is, pseudo-Euclidean metrics

space-time, which is used in the special theory

of relativity. The metric allows to determine the distance of points in space,

the Lorentz metric it is necessary to take the square root of the result of subtraction

from the square of the time coordinate of the sum of squares space. In this

case passengers are treated as events in (1+1)-dimensional space: if the couple

passengers are able to prevent the passage each other, they are separated

bremelatonine interval, if not able to use

at the same time prostranstvennogo.

For small values

the number of passengers, the authors obtained analytical estimates of the performance

different strategies, and for large — analyzed using computer

model. It turned out that the most profitable to follow the rule “first

slow”, as it provides the highest average parallelism: while

sit last slow, fast also the first time to find its place.

Strategy “first

slow” turned out to be 28 percent better than the “first quick”, which became

second, they were followed by random disorganized boarding, and “from tail to nose” showed themselves the worst. Moreover, scientists call received

the outcomes of the universal within the constraints of the model in which

considered three parameters: the proportion of slow passengers, excess necessary

them for planting time and density of passengers in the aisle between the seats.