MATHEMATICAL MODELING OF THE MOTION OF GROUPS OF PEOPLE DURING EVACUATION FROM BUILDINGS

Abstract

The problems of cutting and packing (C & P Problems) have been actively studied by the scientific community over the past years. This interest is explained both by their great complexity from a theoretical point of view, and by a wide range of their application in solving urgent practical problems, for example, in informatics, logistics, modeling of production processes, ensuring the safe life of the population, etc. One of the most important issues in ensuring the safe life of the population is the timely evacuation of people who find themselves in a life-threatening situation. To carry out operational and tactical actions to evacuate and rescue people from buildings, fire and rescue units are created, which, as a rule, are formed according to the type of emergency that has arisen in the building, that is, according to their professional orientation. At present, fire and rescue units are being helped by software systems for controlled evacuation from buildings, the main component of which are programs for simulating the movement of the human flow, which at each fixed moment of time represents the configuration of the placement of people. In practice, the problem often arises of modeling the movement of people in groups, examples of which are family members or rescuers of one unit who move with a load. Therefore, an urgent task is to model the movement of groups of people, taking into account the maximum permissible distances between members of groups and who are evacuated with a load. The paper proposes a model of a human body with a load, which is a two-component complex object in the form of a union of an ellipse and a rectangle, between which the maximum allowable distances are set. Taking into account the maximum allowable distances between objects allows you to combine them into subgroups, and the specified maximum distances between subgroups allows you to combine them into groups. The listed restrictions on the interaction of objects are formalized, a mathematical model of the actual problem of modeling the movement of people with their division into groups is built. For the analytical description of the conditions of non-intersection of objects, the apparatus of quasi-phi-functions of composite objects is modified, which are the basis of algorithms for modelingindividual flow movementof people.