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,
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.
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.