Methods of modeling the flow of visitors at public events

Abstract

This study aims to improve the visitor experience at large-scale mass events. The risks associated with emergencies at mass events can be significantly reduced with information-driven access control systems. In this context, a pressing research objective is to develop a mathematical model of visitor flow movement at the event area entrances and exits. The model for the passage of arriving visitors through the turnstiles is a multi-channel queuing system with unlimited queues. In this case, the flow of requests is not constant. A queuing system with varying inflow intensity can be modeled by approximating the inflow intensity using continuous piecewise functions. The paper describes numerical and numerical-analytical solution methods for the problem of finding state probabilities. The pedestrian movement model as they leave the event venue can be described by a multi-channel queuing system. The request flow and service time are distributed according to Erlang's law. The stationary probabilities of the system states are found by Markovization using the pseudo-state method. The authors present an algorithm for finding the stationary probabilities of the system using recurrent relationships and a method for calculating service organization quality characteristics for participants leaving the event area. The conclusions can be applied to the automated regulation of visitor flows using digital information panels.