FUZZY MODEL FOR THE MAXIMUM DYNAMIC FLOW FINDING FOR SOLVING THE TASK OF EVACUATION FROM BULDINGS
Abstract
This article is devoted to solving the important task of evacuation from building, particularly,
evacuating the maximum number of victims from dangerous areas to safe ones within a given time interval.
The constructed model of the evacuated building is represented by a transportation network with a
dynamic structure, since the capacities and parameters of the flow time can vary in time. In addition, thenodes of the transportation network have weights that limit the maximum number of people who can be
arranged in a given vertex-room. The fuzzy and uncertain nature of the network parameters leads to the
problem statement in fuzzy conditions, which allows simulating a real evacuation situation, in which the
arc capacities in different time intervals are not exactly determined, however can be estimated approximately,
in a certain interval, etc. This leads to the necessity of the specifying arcs in a fuzzy form. A feature
of the algorithm is the ability to take into account the weights of the vertices of the transportation
network; this is accomplished by replacing the vertex with the arc capacity with two auxiliary vertices,
the arc between which has capacity equal to the initial capacity of the vertex. The numerical example
illustrating the operation of the proposed algorithm is solved. The results obtained in the course of solving
the evacuation task using the proposed algorithm can be applied in practice to solve the building
evacuation tasks in uncertain conditions, where the exact number of evacuees is not known and the
maximum possible number of evacuees must be transferred to safe zones, taking into account the timevarying
capacities and limitations on the capacity of the rooms.
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