Experiment and multi-grid modeling of evacuation from a classroom

The evacuation process of students from a classroom is investigated by both experiment and modeling. We investigate the video record of the pedestrian movement in the classroom, and find some typical characteristics of the evacuation, including variable velocity, dislocable queuing, monopolizing exit and so on. Based on the experimental observation, we improve the multi-grid model by considering the pre-movement time of each pedestrian, adopting variable velocity and using a new update procedure. With the improved multi-grid model, we simulate the evacuation process and compare the simulation results with the experimental results, and find that they agree with each other closely. In order to analyze the uncertainty of evacuation, we investigate the influences of the pre-movement time and its distribution on the evacuation. It is found that the evacuation times exhibit a (truncated) normal distribution and vary within a region of about 30% of the mean value. An interesting phenomenon is that the evacuation time of the egress experiment is close to the minimum value calculated with the model, due to the coordination among pedestrians during the experiment. The study may be useful in developing applicable egress models and understanding the basic egress behaviors.     

Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing

In this study, experiments of single-file pedestrian movement were conducted and the movement parameters of pedestrians were extracted with a digital image processing method based on a mean-shift algorithm. The microscopic characteristics of pedestrian dynamics, including velocity, density, and lateral oscillation, as well as their interrelations, were obtained and analyzed. Firstly, we studied the lateral oscillation phenomena of pedestrian movement. The result indicates that the trajectory of pedestrians presents a wavy form and the amplitude of the oscillation remains about 5.5 cm when the pedestrians move with free walking velocity, which is the velocity when there is no obvious interaction between sequential pedestrians; but when the movement velocity decreases to 0.27 m/s, the amplitude of oscillation increases to 13 cm. With increasing density, the velocity decreases and the amplitude of oscillation presents a linear increase trend. The increasing oscillation amplitude widens the occupation area of a pedestrian with low velocity, so as to make the moving efficiency even worse. Secondly, we studied the frequency of the oscillation; the result indicates that the frequency remains at 2 Hz when pedestrians move with a free walking velocity, but it presents a similar linear decrease trend when the velocity changes to a lower value. The decrease of oscillation frequency is also a negative feedback to the moving efficiency. Thirdly, it is found that with the increase of crowd density, the time interval between two sequential pedestrians increases, though the space gap between them decreases. The quantitative relation between time interval and crowd density is obtained. The study in this paper provides fundamental data and a basic method for understanding pedestrian dynamics, developing and validating evacuation models. The results are also expected to be useful for evacuation design.     

Experiment and modeling of exit-selecting behaviors during a building evacuation

The evacuation process in a teaching building with two neighboring exits is investigated by means of experiment and modeling. The basic parameters such as flow, density and velocity of pedestrians in the exit area are measured. The exit-selecting phenomenon in the experiment is analyzed, and it is found that pedestrians prefer selecting the closer exit even though the other exit is only a little far. In order to understand the phenomenon, we reproduce the experiment process with a modified biased random walk model, in which the preference of closer exit is achieved using the drift direction and the drift force. Our simulation results afford a calibrated value of the drift force, especially when it is 0.56, there is good agreement between the simulation results and the experimental results on the number of pedestrians selecting the closer exit, the average velocity through the exits, the cumulative distribution of the instantaneous velocity and the fundamental diagram of the flow through exits. According to the further simulation results, it is found that pedestrians tend to select the exit with shorter distance to them, especially when the people density is small or medium. But if the density is large enough, the flow rates of the two exits will become comparable because of the detour behaviors. It reflects the fact that a crowd of people may not be rational to optimize the usage of multi-exits, especially in an emergency.     

Effect of vertical grouping behavior on pedestrian evacuation efficiency

Grouping behavior is an important element which affects pedestrian group-moving behavior significantly. Current studies only give a few discussions on how grouping behavior affects pedestrian counter flow, while the effect of grouping behavior on evacuation flow is largely ignored. Here we propose a cellular automation model to describe pedestrian behavior under different grouping behavior in evacuation. By simulation we find that, comparing with other grouping behaviors, vertical grouping will block pedestrian transverse movement significantly, and this may cause pedestrians to appear as a two-peak arching distribution in the middle of evacuation and two-peak arching with a gap distribution near the end of evacuation. To the best of our knowledge, this is the first time these phenomena have been presented.     

A novel algorithm of simulating multi-velocity evacuation based on cellular automata modeling and tenability condition

A cellular automata (CA) model, which adopts the findings of tenability analysis, is proposed to simulate the evacuation from a smoke-filled room. Two algorithms, viz., direct algorithm and indirect algorithm, are used to model the behavior of a crowd consisting of people with different movement velocities. In the indirect algorithm, the movement velocity is related to probability so that the CPU time is greatly reduced. Another novelty is that an experimental formula for estimating the survival duration when exposed to constant concentration of toxic gases in a static environment is extended to one that involves varying degree of toxic gases. This has been incorporated into the CA model.     

Aggregate-level demand management in evacuation planning

Without successful large-scale regional evacuations, threats such as hurricanes and wild-fires can cause a large loss of life. In this context, automobiles are oftentimes an essential transportation mode for evacuations, but the ensuing traffic typically overwhelms the roadway capacity and causes congestion on a massive scale. Congestion leads to many problems including longer, costlier, and more stressful evacuations, lower compliance rates, and increased risk to the population. Supply-based strategies have traditionally been used in evacuation planning, but they have been proven to be insufficient to reduce congestion to acceptable levels. In this paper, we study the demand-based strategies of aggregate-level staging and routing to structure the evacuation demand, both with and without congestion. We provide a novel modeling framework that offers strategic flexibility and utilizes a lexicographic objective function that represents a hierarchy of relevant evacuation-based goals. We also provide insights into the nature and effect of network bottlenecks. We compare our model with and without congestion in relation to tractability, normative optimality, and robustness under demand uncertainty. We also show the effectiveness of using demand-based strategies as opposed to using the status quo that involves a non-staged or simultaneous evacuation process. Effective solution procedures are developed and tested using hypothetical problem instances as well as using a larger study based on a portion of coastal Virginia, USA.     

Modeling of pedestrian evacuation based on the particle swarm optimization algorithm

By applying the evolutionary algorithm of Particle Swarm Optimization (PSO), we have developed a new pedestrian evacuation model. In the new model, we first introduce the local pedestrian’s density concept which is defined as the number of pedestrians distributed in a certain area divided by the area. Both the maximum velocity and the size of a particle (pedestrian) are supposed to be functions of the local density. An attempt to account for the impact consequence between pedestrians is also made by introducing a threshold of injury into the model. The updating rule of the model possesses heterogeneous spatial and temporal characteristics. Numerical examples demonstrate that the model is capable of simulating the typical features of evacuation captured by CA (Cellular Automata) based models. As contrast to CA-based simulations, in which the velocity (via step size) of a pedestrian in each time step is a constant value and limited in several directions, the new model is more flexible in describing pedestrians’ velocities since they are not limited in discrete values and directions according to the new updating rule.     

Ranking robustness and its application to evacuation planning

We present a new approach to handle uncertain combinatorial optimization problems that uses solution ranking procedures to determine the degree of robustness of a solution. Unlike classic concepts for robust optimization, our approach is not purely based on absolute quantitative performance, but also includes qualitative aspects that are of major importance for the decision maker.We discuss the two variants, solution ranking and objective ranking robustness, in more detail, presenting problem complexities and solution approaches. Using an uncertain shortest path problem as a computational example, the potential of our approach is demonstrated in the context of evacuation planning due to river flooding.     

Small-grid analysis of discrete model for evacuation from a hall

 In this paper, small-grid analysis of discrete model is described, and simulation that some walkers leave a hall is carried out to check the effects of different desired walk velocities with the same walk time at a time step, and different numbers of small grid at a time step with the same desired walk velocity, on the evacuation time. The simulation results show that small-grid analysis have reproduced some typical phenomena of evacuation, including jam, block and faster-is-slower, etc. as good as the continuum model, i.e., the social force model, but with high simulation efficiency. In addition, the power-law distribution of evacuation flow duration and block duration with the different desired walk velocities is found. The block duration with different numbers of small grid at a time step also takes on power-law characteristics, only their intercepts in log–log coordinates are different.