Building a model and an algorithm for modeling the movement of people carrying goods when they are evacuated from premises

Evacuation is often the only way to save a person who is in a life-threatening situation. At present, evacuation software is used to simulate the movement of human flows, which does not always reflect the real processes of their movement. Therefore, it is a relevant task to build models for modeling the movement of human flows for different types of emergencies, different categories of human movement, and various spatial forms of their representation. Such a task arises when evacuating people from premises for various functional purposes. During evacuation, people often carry some goods. When people move carrying some goods, their horizontal projection takes a more complex shape than an ellipse or circle considered in earlier studies. Moreover, in practice, there is often a task to model the movement of people taking into consideration the maximum permissible distances between them. This paper reports the new quasi-phi functions of interaction between the ellipse and rectangle accounting for the maximum allowable distances between them. The proposed mathematical apparatus has made it possible to formalize the interaction between objects, thereby enabling the construction of a well-substantiated mathematical model, as well as the methods and algorithms for modeling the movement of people carrying some goods. The possibility to simulate the movement of people with certain objects has shown taking into consideration the maximum permissible distances between them. A test example of the movement of people along four corridors was simulated, in each of which there were 28 people subsequently merging into one flow. Given the uniform distribution of three types of cargo: «backpacks», «suitcases», and «bags on wheels», the movement slowed down by about 4 %. When half of the evacuees had «bags on wheels» that can move away from people at arm’s length, the slowdown was about 6 %