Modeling of emergency evacuation in high rise buildings considering congestion at stairs based on Markov chains

High-rise buildings are vulnerable to encountering fires or other emergencies at any time, requiring an immediate evacuation of occupants. In the context of building evacuations, various engineering parameters are often utilized to evaluate the time required for people to reach a safe place when descending a staircase. A discrete-time Markov chain model is proposed to evaluate the evacuation time of the occupants in such circumstances by taking into consideration factors like merging at the stairs and congestion on the floor. Based on the congestion probabilities with respect to the number of evacuees in the building and other human behavior factors that slow down the rate of evacuation, non-congested and congested scenarios are evaluated. The effect of the critical parameters that influenced the evacuation process in the high-rise building, such as walking speed, number of evacuees, and effective stair width, is evaluated in both scenarios. The findings indicate an optimal evacuation speed of 0.7–1.4 m/s. The effective width of the stair is suggested to be between 1.6 and 2.4 m using the model. The simulation results are in good accordance with the SFPE method, the NIST egress simulator, and the agent-based model results.