A mathematical model of pedestrian movement on the basis of the stochastic cellular automata approach is proposed. A floor field (FF) model is taken as a basis model. The FF models imply that virtual people follow the shortest path strategy; meanwhile, they also follow the shortest time strategy. The focus of this study is mathematical formalization and model implementation of these features of pedestrian movement. Some results of the simulation are reported.

Space-planning decisions of two sports and entertainment arenas with large crowds—the Roman Colosseum (Italy) and the modern Gazprom Arena stadium (St. Petersburg, Russia)— were analyzed to compare the flow of people during evacuation by simulation. It was shown that the space-planning decisions of the Colosseum seem more advantageous compared with the Gazprom Arena in calculation of evacuation time and evacuation organization process: the capacity of the stairs of the Colosseum with a width of 2.8 m is comparable with the capacity of the Gazprom Arena’s stairs (4 m). In the Colosseum the average specific flow is q_average = 1.14 person/s/m, while in the Gazprom Arena the average specific flow is q_average = 0.65 (with a march width of 2.6 m) and q_average = 0.8 person/s/m (with a march width of 4 m). It was found that the Colosseum complies with current standards for on-time evacuation; while modern sports and entertainment arenas are currently designed with additional services, infrastructure, comfort and, in general, high commercialization. The antique arenas are currently being reborn and used for concerts and other public events, so the obtained results have practical significance.

The manuscript is focused on the problems of evacuation in case of fire from the buildings of museums as places with a mass presence of people. Features specific to museums and how they affect safe evacuation conditions are discussed. Most attention is paid to evacuation management, since the vast majority of museum visitors are not familiar with the layout of the building. In this case, the actions of staff in evacuation management are decisive. The paper considers the development of evacuation schemes, taking into account the spread of fire hazards in the building and the development of instructions on their basis for the staff. Using the example of the Winter Palace of the State Hermitage Museum, the solution of the marked tasks with the use of computer simulation of evacuation during a fire is given. The analysis of the simulation results showed the vulnerabilities of the museum. In this work, the evacuation schemes for the scenarios are considered. The maximum number of visitors at a single time in the Winter Palace has been set at 4000. The principles of making evacuation schemes are formulated, including taking into account the peculiarities of space-planning solutions inherent in museums, such as enfilades and the connections of rooms.