By applying the probabilistic method and optimization synthesis of flexible technological lines, topological models have been built of safety-oriented management of human flows and evacuation time using the «Arena Lviv» stadium as an example. They are necessary to calculate the time of evacuation of people to a safe zone. When people leave the stadium sectors on the promenade, their flow is significantly modified. Therefore, the calculation of the time of evacuation of people requires the use of different procedures depending on the type of human flow in order to obtain more accurate results. There may be several such cases on one evacuation route and significantly more during the evacuation of people from all sectors and premises of the stadium administrative building as a whole. Thus, a lot of time is spent on choosing the right procedure and initial data for calculation if we use existing classical verbal models, which is their disadvantage. Verbal models have a large volume, they need to be repeatedly re-read in order to determine the numerical values of factors affecting the flow of people while topological models are much more compact. Topological models make it possible to visually present more complete information about the evacuation process, and this makes it possible to quickly select the initial data for calculating the time of evacuation of people at the next evacuation site. The time of evacuation of people from the «Arena Lviv» stadium was calculated; the evacuation system happened to not comply with the accepted standards. In particular, the time of evacuation of people from the structure exceeded eight minutes. Using the critical path method, bottlenecks of the stadium evacuation system were identified, and human flows were redistributed, which made it possible to reduce the total evacuation time to acceptable indicators
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