This paper discusses features of automated checkpoint systems (ACS) turnstiles dynamics in public venues and mass gathering events. Turnstiles are servers from the point of view of queuing systems theory. Stages of visitors exit from the facility at the end of the event are studied. The server mathematical model and the flow of clients arriving at the input of a server are described. Estimates of the maximum queue length and the maximum waiting duration for leaving the mass gathering events venues for two different policies of visitor behavior have been obtained. Scientifically proven recommendations for the behavior of visitors when leaving the facilities of public events are given.