The only time I have been to Mumbai, earlier known as Bombay, was during the year 2010. There are many things that the densely populated city of Bombay is known for, but what I am going to talk about is my experience during my visit to the suburban railway station. The commuter-populations in these railway stations and inside the trains are nothing short of ‘crazy’ with densities as high as 14-16 people per square meter. There is an old saying about the railway station experience in Bombay paraphrased as:
“The crowd takes you in and the crowd takes you out, you do not have to do anything”.
In the railway station in Bombay, I experienced this firsthand! When I was waiting to get into the train, the restless crowd began to move towards the compartment door of the train as it slowed down. There was a very strong counter-current flow as the already packed train unloaded some of its passengers and simultaneously, the people waiting to board the train got in rather hurriedly, trying to find some space in the train. When I managed to squeeze myself and go close enough to the compartment, the crowd that was moving into the train just forced me into it. It was almost as though I was carried into the train’s compartment. The train slowly took off that eventually forced the people who were still entering and exiting the compartment, to move away from it.
After a ride in the packed compartment, the next station arrived. Now I was not getting down there, but as the train was about to stop, movement had already begun inside the compartment and very soon there was a strong flow of people out of the train. I knew if I did not get away from the flow, I would be trapped and taken out of the train with no guarantee of making it back in. Well, it was one heck of an experience! Something I would never forget in my life. But little did I know that this memory would spark an interesting problem to study several years later.
A video of a Bombay Railway station at peak hour (courtesy: LPE360 Clip Licensing)
Many years later…
I came across an interesting title, ‘freezing by heating…’, a letter in PRL by Helbing and coworkers. While I was going through the model described in the article, trying to understand how the interactions led up to the phenomenon of ‘freezing’ as ‘temperature’ increases, I soon got distracted by the apparent simplicity of the model. It was a composite crowd of agents (circular discs on a plane) made up of two types: one that wants to travel in the +x direction and the other in the -x direction, with the same speed. Developing a fond interest in the model, I soon coded it in MATLAB and started making visualizations of the dynamic behavior of the agents. I saw many interesting things like, the agents colliding with each other as they struggled to move in the direction with the speed they desired to move in, some agents getting trapped and entrained in the counter flow of agents of the other type and agents through collisions beginning to self-organize to form lanes.
Depending on the initial conditions and choice of parameters, the crowd model shows interesting collective phenomena.
Immediately I saw the connection—these agents, in my simulation, were very much like the passengers in the Bombay railway station! Individuals who got caught as the commuter-crowd moved towards, or from out, of the train compartment were like the agents in the simulation which got entrained in the counter flow. I soon realized that this problem was not limited to Bombay’s railway stations. But a common problem in crowded places, like say pilgrimage sites in Tirupati, Mecca, etc. It was remarkable how a model with agents that followed rules rather ‘mindlessly’ were able to capture the qualitative features of a group made up of human beings with advanced cognitive faculties.
The crowd phenomenon though very interesting and captivating from the perspective of group-behavior, poses a serious safety issue—stampedes. I wondered if I could use the agent-based models to understand the scenario better and if possible, devise a mitigation strategy. I asked myself this question—can a person sitting before a monitor, observing the CCTV camera feed, be able to differentiate commuters readily moving in the direction of the crowd from those who are forced to move against their volition? Maybe the person can. Since, humans are, in general, good at identifying patterns and features. But it would be impossible for a human observer to go through data continuously and to cover large spaces you would need multiple such observers. Instead, think of a computer observer, handling continuous feed of data of the movement of commuters, extracted through computer vision and object tracking. Can this computer observer guess which group an agent belongs to, from simply the movement information of the commuters? I realized that the answer to this question was not straightforward and hence I did what most researchers generally do—study the problem in a simple idealized setting.
I took the model from Helbing and coworkers, made suitable changes, and ran simulations for a variety of parameters that included, how densely the agents were packed, the number ratio of agents in each group, desired speed of motion. Following this, I fed all the data from the simulation, except the agent’s group identity, to an ‘observer model’ whose aim was simply to predict the group identity from the information fed. The observer model called an agent moving in one direction (+x) as belonging to one group and the others moving in the opposite direction (-x) as belonging to the other.
Two different observers that were studied
I found that even under idealized settings, and regular agent-behavior, the group-identification problem was non-trivial. Under some cases where agents self-organized to form distinct lanes, the identification was accurate. But in general, the collisions between agents resulted in misclassifications. It was even more intriguing to find that the accuracy of classification non-monotonically depended on the properties of the system. In one scenario, it was found that agents got misclassified more when they tried to move past each other faster: similar in nature to the well-known ‘faster is slower’ effect observed in pedestrian systems. I was able to understand why only in some instances classification was effective from the microscopic dynamics of agents. Then my student came along, and asked: why not use the information available on the neighbors to classify the agent as belonging to one group or another? Afterall, agents are pushing each other as they move, just like the people pushing each other in the crowd. The crowd either aids in the motion of the agent or resists it and hence the state of the neighborhood encodes information of the identity of the agent that the observer wishes to classify. Using this idea, we developed a new neighborhood observer which was able to classify the agents accurately even if they were entrained in counter flow.
I would have never imagined that I would be modeling or studying a problem motivated by a life experience, which at first sight would appear seemingly unconnected to chemical engineering (the discipline I belong to). I worked on droplet flows in microchannels for my PhD. But a closer look, with an open mind, would reveal the similarities between inanimate particle/droplet movement and the motion of pedestrians/traffic. And once you see this similarity, it is only a matter of time before you adopt the problem as your own and begin to approach it with techniques and analyses native to chemical engineering.
I haven’t solved the actual problem yet! But even in an idealized setting the problem of identifying agent-identities was far from trivial and has taught me many things. Will the findings of the study help me or the community to solve the real problem at hand?—preventing a stampede or identifying persons who need immediate attention—only time will tell.
Relevant literature:
A news article explains Bombay railway station’s population explosion:
Helbing’s article on “Freezing due to heating in a driven mesoscopic system”:
Our article on, “Observing a collective to infer the characteristics of the individuals”: