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Understanding crowd dynamics at ghat regions during world's largest mass religious gathering, Kumbh Mela
Author’s Accepted Manuscript Understanding Crowd Dynamics at Ghat regions during World's Largest Mass Religious Gathering, Kumbh Mela P S Karthika, P M Aparna, Ashish Verma www.elsevier.com/locate/ijdr
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S2212-4209(18)30509-0 https://doi.org/10.1016/j.ijdrr.2018.08.005 IJDRR961
To appear in: International Journal of Disaster Risk Reduction Received date: 21 April 2018 Revised date: 8 August 2018 Accepted date: 8 August 2018 Cite this article as: P S Karthika, P M Aparna and Ashish Verma, Understanding Crowd Dynamics at Ghat regions during World's Largest Mass Religious Gathering, Kumbh Mela, International Journal of Disaster Risk Reduction, https://doi.org/10.1016/j.ijdrr.2018.08.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Understanding Crowd Dynamics at Ghat regions during World’s Largest Mass Religious Gathering, Kumbh Mela
P S Karthikaa, P M Aparnab, Ashish Vermac* a
Research Scholar, Department of Civil Engineering, Indian Institute of Science (IISc), Bangalore - 560012, India Email: [email protected]
b
Project Associate, Department of Civil Engineering, Indian Institute of Science (IISc), Bangalore - 560012, India Email: [email protected]
c
Associate professor, Department of Civil Engineering and Robert Bosch Centre for Cyber Physical Systems, Indian Institute of Science (IISc), Bangalore-560012, Karnataka, India. Email: [email protected] * (Corresponding Author) Abstract In this paper a porous flow approach on a cul de sac is proposed to understand the dynamics of crowd at ghat regions (banks of the sacred river) in mass religious gatherings. Kumbh Mela, one of the mankind’s largest religious gathering encompassing almost all possible crowd scenarios, provides a unique opportunity to explore the crowd dynamics along all facets. Here, Cul-de-sac refers to the ghat region where people gather with the intention to take holy dip. The data used for this study was collected during Kumbh Mela held during 22nd April to 21st May 2016. Visual observations from the video data shows a high degree of complexity probably due to the nature of activities at the study location, e.g., lane formation, creeping behaviour etc. The proposed porous flow approach divides the entire study area into pores, and it is assumed that pilgrims traverse this network through interconnected vacant pores. The pedestrian data from video sequences (entry time, exit time, and flow) is extracted manually and time series analysis of pore occupancy is done to get an approximate measure of local density. Further, using Poisson regression analysis it was found that both the inflow and the duration of holy dip are significant factors in influencing the number of arrivals into the pore. Since behavioral aspects of a pedestrian is a significant governing factor of crowd dynamics, these microscopic parameters can be used to get a measure of criticality of the system in terms of crowd risk.
Keywords: Crowd dynamics, Porous flow, Occupancy, Arrival pattern of pedestrians, Kumbh Mela, India
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Introduction A crowd is referred to as a group of heterogeneous people congregated or collected into a closed body without order, characterized by a common interest. World Health Organization [3] defines mass gatherings as “more than a specified number of persons at a specific location for a specific purpose for a defined period of time”. Although crowd dynamics has been extensively studied, there is still scope for investigating different behavioural aspects purely because uncertainty is inherent where humans are concerned. The challenges imposed by this uncertainty in the behaviour of the crowd translates into panic situations, resulting in large casualties. Developing economies are observed to be more prone to fatalities from crowd risk situations in such mass gatherings. Religious gatherings and pilgrimages have been venues for 79% of stampedes in India (Illiyas et al., 2013). In India, with its diversity in religion, language and culture, numerous religious festivals are celebrated every year resulting in large number of mass gatherings. A few of these include Kumbh Mela, Sabarimala pilgrimage, and Godavari Maha Pushkaram. Among these, Kumbh Mela is the mankind’s largest gathering, where an estimated 75-100 million people visit the event site in a span of one month. This could also be attributed to the fact that India is the second most populous country in the world. Considering all these, studying the crowd dynamics at mass religious gatherings is highly relevant and important to improve crowd safety. This study aims at understanding the crowd dynamics at ghat regions (river banks) in Kumbh Mela held in Ujjain during 22nd April to 21st May, 2016, popularly known as Simhasth-2016. Kumbh Mela is a mass Hindu pilgrimage held at four different places, namely Haridwar, Ujjain, Nasik, and Allahabad, every three years. Most of the earlier Kumbh Mela’s have been marred by events resulting in loss of lives and large number of casualties. The last Kumbh Mela held in Ujjain, during April-May 2016 witnessed a natural calamity resulting in 7 deaths. Similarly, crowd crushes have taken a toll of 36 lives in Kumbh 2013, 39 in Kumbh 2003, 50 in Kumbh 1986, and 800 in Kumbh 1954. These numbers are indicative of the sensitivity of the crowd in expediting the risk factors and thereby triggering stampedes. An extensive review of the literature on the various studies on crowd is beyond the scope of this paper. The authors would however, like to highlight a few studies which are relevant to the present work. As mentioned previously, there is a large body of work available in the area of crowd behaviour. In general, the pedestrian models are usually characterized according to the scale of the variables used in the model as microscopic, mesoscopic, and macroscopic. The macroscopic approaches associate pedestrian flow to the flow of fluids and gases, without explicitly modeling the individuals and their interaction. The microscopic models on the other hand focus on the individual entities and their interactions with other individuals and the environment. The 2
mesoscopic approaches model the pedestrian movements and their interaction through averaged out quantities, making them computationally more efficient than microscopic models (Johansson, F. 2013). A variant of this is the behavioral-social dynamics model proposed by Bellomo, N. et al.,(2015) where the pedestrians belong to one particular group (known as the “functional subsystem”) based on a variable called,”activity variable”. This is a part of the microscopic state of the pedestrian along with the position, and velocity. The interactions between the pedestrians are modeled through the transition probability density that changes the activity variable. Here, it is possible to account for the different emotional states of pedestrians based on the strategies adopted by the individual. A previous study on the crowd behavior at Kumbh Mela by Ubboveja et al., (1992) concentrated on the qualitative aspects of pedestrian traffic. It was found that a high level of potential risk existed during different timings at various locations in Kumbh Mela 1992. The author developed a simulation model to evaluate psychological behavior and introduced a parameter PRI (Psychological Rating Index) which is a numerical value for exhibiting the instant psychological potential risk levels at any location. One important behavioral characteristic identified is that the density is not the only criteria for the explanation of crowding behavior and crowd risk level. Rush and surge of people, accidents, natural or human induced hazards, rumors, competition of procurement, sudden change of entry/exit points, end-of-event exit or beginning-of-event surge are the sources of crowd disturbances and triggering factors of crowd crush, which were identified from the case studies (Illiyas et al., 2013). A similar study on Hajj devotees by Johansson et.al (2008) also points out that neither the density nor the speed or flow field are good measures of the criticality in the crowd. Another study conducted in Mina also highlights the lack of understanding about the characteristics and behavior of pedestrians in cases of high density crowd dynamics (Dridi, 2015). Hariharan et al., (2017) emphasized on the need to conduct studies on mass religious gatherings in an uncontrolled setup as the circumstances are very dynamic and different from a controlled experimental setup. For the safety of pilgrims in mass religious gatherings, to ensure an early response to any emergency situation/problem, or to predict an emergency situation/problem, a sophisticated and continuous monitoring system like an early warning system is very much required. Various experiments serving as input to mathematical model which can be formulated to calculate crowd risk index (CRI). The current state of the system coupled with simulations based on route choice algorithms will provide a feedback to the CRI and this value can possibly be used by event managers to manage crowd to increase crowd safety. All these studies have emphasized on the need to understand the crowd dynamics at high densities much more rigorously.However, literature consisting of studies to understand crowd dynamics using real field data at mass religious gatherings is sparse. Most of the studies on crowd behaviour is also concentrated on experimental data. The present work intends to focus on 3
one particular type of gathering, a mass religious gathering known as “Kumbh Mela”, where people don't hesitate to barter their personal safety for a chance to be a part of the gathering. . The following are the objectives of the study. ● To understand the crowd dynamics at ghat regions by studying the different patterns of movements exhibited by the pedestrians and to conclude possible explanation for these visual observations ● Develop a conceptual framework for modeling the observed flow patterns with the help of analogous system using the insights derived from general observations ● Understanding the relation between macroscopic parameters of pedestrian flow ● Interpreting the microscopic behavior of pedestrians using parameters such as pore occupancy, arrival rate of pedestrians, and duration of holy dip The paper is organized as follows. The upcoming section gives an overview of the data collected and the importance of the location at which the data is collected. Based on the observations, goals defining the study have been identified in the next section. The following section describes the conceptual framework. Analysis and results are discussed in the next section, and the final section highlights the merits and shortcomings of the study. Data Collection The data used in this study was collected in Kumbh Mela 2016 in which an estimated 75 million people participated during a span of 1 month. The field work was done for 30 days, from 22nd April 2016 to 21st May 2016. Video recordings were taken at different locations including corridors, river banks and intersections. From the video recordings, the study section was chosen such that the people could be observed with clarity as to how they conduct themselves at ghat regions. The pedestrian data used in this study was collected by video capturing the pedestrian flow at Ram ghat, considered to be the most auspicious location for holy dip, on 9th May 2016, also known as “Shahi Snan” day. This particular day is chosen for the analysis since it is marked with highest inflow during the whole event. The next section provides a brief overview of the location considered for the analysis to get an understanding of the feel of the crowd and their associated activities. Cul-de-sac Generally, Cul-de-sac refers to a street or passage closed at one end. Here, it means a nonthrough space providing access for people who intend to take holy dip. The event can be described as a gathering of people for a common purpose by some prearrangement. Huge numbers of pilgrim’s flock to the ghat regions with a belief to cleanse themselves of their sins by taking holy dip in the sacred river. Unique crowd dynamics is thus created, when the entire crowd moves towards the river to take holy dip, at the Ghat area. Since most of these pilgrims come in groups, they spend considerable amount of time at the banks for every one of them to conclude their activities. It is like a system that contains a number of companion clusters where 4
people arrive, remain and leave together. The participants show a great variation from the most privileged sadhus (holy men) to the common people from rural areas. On special days of holy dip, the crowd density at ghats become extremely high. The data has a high degree of complexity due to the nature of activities at the study location. Here, the microscopic behavior of pedestrian movement is of great utility in gaining an understanding of the macroscopic state of the system. This is especially true in the studied situation where the change in trajectory of a single pedestrian has the ability to change the flow dynamics at least locally. Also, the space utilization of the crowd when observed at a macro level is highly uneven. This could be ascertained by modeling the changes in local densities. By studying the different patterns of movements exhibited by pedestrians in a crowd, it will be possible to understand the crowd dynamics and thereby provide more insights on the critical parameters to be used in simulation. Snapshots of the study section is shown in fig 1. A number of interesting points about crowd dynamics were visually observed from the data and could be noted by plain visual observation of the video data as summarized. ● Unlike vehicular traffic, multi directional pedestrian movement is observed in a single lane ● Crowd continues to move even at higher densities. This same phenomenon is observed by Johansson et al., (2008) in Mina ● Pedestrians tend to move in groups similar to platoons, the group sizes varying from 2 to approximately 8. The different groups interact within themselves and with others ● Pedestrians weave themselves into nearly continuous lanes despite the high densities and move seamlessly among each other without experiencing friction ● Backtracking behavior in face of jammed conditions (e.g. due to barricading by police) ● Creeping behavior similar to that in vehicular flow is observed by the acceptance of very small gaps through which sometimes they appear to squeeze through by creating or expanding gaps. Ubboveja et al., (1993) have found that the minimum acceptable gap is as low as 15 cm under controlled movement conditions in a line ● Multiple leaders in a single line itself which results in rather splitting up of formed lanes or merging between two lanes
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Figure 1 Screenshots of ghat areas at Kumbh Mela-2016
Theoretical Framework The conventional way of modeling the parameters in a heterogeneous vehicular traffic is to adopt the same methodology as in homogeneous lane-based traffic with some minor adjustments which are expected to account for the heterogeneity. This results in serious under estimation of the difference in flow patterns occurring as a result of variation in vehicular dimensions, speed and lane indiscipline. In a non- lane-based traffic, be it vehicular or pedestrian, headways and average density are not suitable measures of modeling traffic flow. In the present context, with multi directional, haphazard sort of pedestrian movement and without defined pathways for walking, the same established parameters for defining the distinct patterns produced by pedestrians cannot be adopted. Pedestrian study conducted at railway stations by (Shaha et al., 2013) tries to understand the fluctuations in pedestrian flow depending on the arrival and departure of trains. This study, though not in the context of mass religious gatherings have similarities in the pedestrian behavior in Kumbh Mela as even here people carry luggage, they travel in groups, and they are goaloriented. The study shows different speed – flow trends at different size staircases. Nair et.al (2012) has proposed a novel porous flow approach for traffic flow modeling, where pores are defined as spaces between vehicles and roadside. This paper adopts a similar porous flow approach for modeling pedestrian behavior at cul-de-sac. Broadly, this approach is derived from the flow of fluid through a porous medium. In the study of porous materials, the portion of space not occupied by the soil mass, excluding all those soil pockets or vesicles bounded on all sides by soil particles is considered as pore space. Analogous to the fluid flow through porous medium, the pedestrians are assumed to navigate through the study section represented as a system of pores. Individuals, though being distinct entities, 6
defining boundaries for each individual and their respective groups are difficult as the amount of space occupied by each segment would be different. They actively seek a free path through the crowd instead of being repelled by their neighbors (Moussaid et al., 2011). Instead of defining pores on similar lines, it is our intention to consider the entire study area as partitioned into small pores. At any instant of time, the interest is in the fraction of pores that are empty, as this would give an idea of how pedestrian movements are possible even at high densities if minuscule spaces are distributed throughout the study section creating a network of pathways. For this reason, pores are classified as follows (refer Fig. 2): ▪
Passive pores: pores that are occupied by stationary pedestrians and hence are not free for movement at an instant of time
▪
Active pores: pores that are free for pedestrians to occupy or readily available for access at an instant of time
Figure 2 Concept diagram showing set of paths at any instant of time between origin and destination
A particular feature of the pedestrian flow in the ghat regions is the distinction between stationary and moving pedestrians. People come to the ghat regions with the aim of taking holy dip. Predominantly, they come in groups, complete their intended activity, wait for all the other members of their group, and then leave together. This forces them to spend some time in the study area with negligible relative movement. The distinctive feature of these activities at ghat regions is the one that allows us to differentiate the system of pores into active pores and passive pores. These are two distinct states through which the state of a pore can be identified. Also, at any instant of time, a passive pore can change to an active pore and vice versa. An important point to be noted is that unlike conventional study, here there is no single origin and destination, but origin and destination are spread out over a length. It is more of an areaorigin (AO) to area-destination (AD). Thus, the problem is defined as modeling the pedestrian flow between an area-origin to area-destination through a system of active pores forming a set of 7
paths. Here, path is defined as a set of connected active pores at an instant of time and the paths are themselves dynamic. At any instant of time, there would be a set of pathways, subject to changes. The interaction between stationary and moving pedestrians results in creation of new paths or an existing path becoming redundant. Therefore, for any individual, who wishes to travel from AO to AD has a set of paths at his departure time from origin. A different kind of user equilibrium exists between these dynamic paths as follows. ● At user equilibrium, all users try to minimize their perceived travel time ● Thus, every used path would have the same perceived travel time ● Users will shift to alternate paths (either created or existing) only if they feel that their travel times are bound to increase if they stay on their path. This can happen if their path is obstructed by some stationary pedestrians or in case of heavy conflicting flow. ● Also, the unused paths are perceived to take longer travel times. These paths will again become active only if either of the previous conditions is met. Modeling the pedestrian flow through these dynamic paths would be a realistic representation of the patterns created while the crowd moves through the study area. As pointed out by Dridi (2015), “Psychology of every individual moving along a street with a specific goal, suddenly changes realizing any obstruction to his goal, influencing his behavior tremendously thereby raising the potential risk level of a group to behave as a crowd.” The following section presents data extraction and results of the study.
Data Extraction The pedestrian data from video sequences obtained from CCTV cameras is extracted manually for duration of 30 minutes. The extracted data include time of entry and time of exit from a pore, inflow into the entire study section (refer fig 3), and the duration of holy dip. The limiting dimensions of the pore are chosen such that at least a single pedestrian is a part of the frame enclosed by the pore boundaries at any instant of time. The approximated area of pore is 0.45 sq. m. This is similar to the minimum area required for a standing pedestrian. As per HCM standards for queuing area (Exhibit 11-9 Queuing area LOS, HCM 2000) required per pedestrian for LOSD is 0.3-0.6 m2/pedestrian.
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Figure 3 Schematic diagram of study section
Number of pedestrian arrivals per unit time data is collected for 30 minutes for a number of pores. This exercise is carried out for another time interval also. The main objective of such an extensive analysis is to understand the spatial and temporal variability of pedestrian arrivals. The duration of holy dip per pedestrian and the incoming and outgoing flow values per unit time are also collected. Heterogeneous traffic in non-lane-based conditions is usually explained by the analysis of headways. Most of these studies propose headways as either exponential distributed or negative binomial distributed (Hossain M et.al, 1999). The same is usually applied to pedestrian traffic also. The next section presents the macroscopic fundamental diagrams obtained from the extracted data. The effect of bin width in deciding the distribution of pedestrian data is presented in the subsequent section. Analysis and Results Figure 4 shows the macroscopic fundamental diagrams at the approach to ghat (referred to as Ram ghat). It could be seen that average speed ranges from 0.8m/s to 1.5m/sec, whereas density varies from 0.8-3.5 ped/m2. The flow values range from 24 ped/m/min to 39 ped/m/min. Unlike the usual flow-density relationships, as density increases the flow remains a relatively constant value. It is also possible that the group behaviour could be a reason for this deviation in the flowdensity relation. A comparison of the flow conditions using experimental data and the field data collected in mass religious gatherings indicates significant differences indicating that the people participating in mass religious gatherings have a common mindset in terms of motivation (Gulhare et al., 2018). Since a uniform relation couldn’t be obtained for the various macroscopic parameters, the data was split into two based on a cut-off value corresponding to the mean flow of 30 ped/m/min. The resulting two flow regimes (fig. 4c) with respect to flow- density relationship show a higher fit in terms of R2 instead of the combined flow conditions (fig. 4d). However, it is important to note that there is no significant variation in the range over which the speed varies for different flow values.
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Figure 4a, 4b: Speed-flow and speed-density diagrams
Fig 4c Flow-density diagram for two regimes
Figure 4d Flow-density diagram for single regime Figure 4 Fundamental flow diagrams at approach to Ram Ghat
Time gaps between successive pedestrians entering a prescribed pore are considered for the analysis of arrival pattern. It is clear from literature that different distributions are proposed for modeling vehicular time-gap by different authors for the same flow range (Dubey et.al, 2012). 10
However, there are only a few studies on modeling the arrival pattern of pedestrians. As a first step, there was a need to ascertain if the pedestrian arrivals into a subset of the area could also be safely assumed as Poisson distributed and to investigate its dependency on the bin width (notated as t). To this purpose, the exercise of fitting Poisson distribution for different bin widths is carried out, and the results are demonstrated using figure 5. The time interval was reduced from t of 60 seconds to a t of 1 second. It could be noted that as the t decreases, the arrivals seem to follow Poisson distribution. The same results were observed when the analysis was done for other pores also. An interesting observation is that dual arrivals show a peaking over single arrivals at all bin widths except for t-5sec. This could be due to two reasons. The first one being the group behavior and the second one being the conflicting arrivals at the same time. It is not possible to identify the groups in detail due to the concentrated movement at the ghat. So, an argument presented to explain this observation is that the 2 arrivals at the same instant of time is the effect of people competing for the same available gap. Therefore, the two arrivals have a higher probability of coming from conflicting flow rather than from the same group, as members within a group have less chance of competing.
A rr iv al fr e q u e n c y o f p e d
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e st ri a n s
Number of pedestrian arrivals Figure 5 Variation in the arrival distribution as a function of the bin size chosen
The effect of pore size and shape variation on the arrival pattern of pedestrians was also investigated. For this purpose, the size of the pore was gradually increased to a point when manually noting the arrival rate of pedestrians were difficult owing to the simultaneous arrival of more than 3 pedestrians into the pore. The shape of pore was also varied to understand the possible variations in arrival pattern. The main conclusion to be drawn from this analysis is that beyond a fixed pore dimension of 0.65 sq. m, it cannot not be considered as a pore in this study. This is because the aim was here to model the gaps that pedestrians are willing to accept, and large pores don’t occur at high densities. Also, in such low flow conditions, there is no need to understand the pedestrian dynamics as people can move freely and complete their activities. In such contexts, the theory of gap acceptance itself is not relevant. The average amount of time that an individual occupies a space has special significance in the ghat region. This is because, holy dip is the primary purpose of visit for majority of the people visiting the Kumbh Mela and hence, the need to understand the amount of time they spend waiting to get a chance or waiting for their group members to complete the ritual. This can also be considered as a kind of area occupancy, where it can be used to relate to macroscopic parameters of flow, namely, density. Here, pore occupancy is defined as the number of pedestrians occupying a pore at any instant of time. Alternately, it could be defined as the percent of time a pore is occupied by a pedestrian relative to the total analysis period. The second definition of area occupancy proposed by Arasan et.al (2008) for vehicular flow is adopted in pedestrian scenario. Either way, the term occupancy could be considered as some measure of local density. Therefore, understanding the variation in occupancy over time is studied in detail. The temporal variation in occupancy for pores placed at different locations in the study area is as shown in figure 6. It could be seen that the highest occupancy is 3 persons/second.
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Figure 6 Occupancy trend plot
It can be observed that at P3 (pore nearer to the ghat), people occupy the same spot for a longer period of time compared to other locations. This may be attributed to the fact that the location 3 is nearer to the ghat and people spend considerable amount of their time at the ghat as they have to wait for all the members of their group to complete the holy dip. The other two locations are along the entry to the ghat and therefore show the corresponding changes in their occupancy patterns. In such locations, rather than modeling the average density over a length it would be better to model the range of concentrated densities at different spatial points in the study area. This would enable us to understand the distribution of local densities and how to effectively tackle these densities. The pedestrian behaviour at the ghat region with pedestrians waiting for their turn to take holy dip amidst the predominantly stagnant crowd is similar to the passenger behavior at railway stations. Dwell time models have been used to study the dwell time of trains (i.e. the time available for passengers to board/alight). It has been generally observed that dwell times can be optimized considering the passenger volume, train design, percentage of standing-through passengers, luggage etc. Here, instead of optimizing the holy dip duration, the effect of duration of holy dip and the inflow into the study area on the number of arrivals of pedestrians into the sample pore is analyzed. This is done using Poisson regression. Arrivals into a pore is assumed to be independent. The count variable, the number of arrivals into the sample pore in a given time interval is assumed to follow a Poisson process whose parameters are decided by the average duration of holy dip in that time interval and the inflow into the study area. Here, yi- the number of arrivals into the pore, ‘i’ (
)
13
The expected number of arrivals per time period is specified log-linearly as
(
)
where,
Two models were estimated, one with inflow alone as the explanatory variable (model b) and the other with both pedestrian inflow and average duration of holy dip as explanatory variables (model a). The estimated parameters are tabulated below. Table 1 Results of Poisson regression
Model a (Unrestricted model) variables Intercept Pedestrian inflow Holy dip duration
Estimate (signf codes) 1.4375 (***) 0.0535 (***) -0.087 (**)
Model b (Restricted model)
Std error
Z-value
0.134
10.720
0.005
9.942
0.0521
0.0278
-3.139
-0.0911
Elasticity
Estimate (signf codes)
Std error
1.319 (***) 0.049 (***)
0.12 4 0.00 5
-
-
Z-value 10.628 9.565 -
LL
-130.84
-137.18
AIC
267.69
278.36
Rp2
0.349
0.288
It could be noted that both the inflow and the duration of holy dip are significant factors in influencing the number of arrivals into the pore. The model (a) shows that as the duration of holy dip increases, the number of arrivals into pore decreases. Comparing the two models, it could be said that the model (a) gives a better fit to the data. The AIC value is lower for model (a) compared to model (b). Also, the Rp2 value of model (a) is greater than model (b). A common test for assessing the two models is the likelihood ratio test. Here, the Null hypothesis, H0: ??hdurn = 0 i.e. Pedestrian arrivals does not vary with the duration of holy dip 14
Elasticity
0.0481
Alternate hypothesis, H1: ??hdurn ≠0 The number of restrictions, R=1. For 1 degree of freedom, at 95% confidence level is 3.84. ??????=12.67> . Therefore, there is sufficient evidence to reject the null hypothesis. It could be concluded that the unrestricted model (Model a) is better than the restricted model (Model b). The final model is therefore, given by
As the duration of holy dip per individual increases, the pores near to the ghat gets blocked resulting in a further decrease in the number of arrivals. This block could be the result of two reasons: either they are waiting for their group members to complete the ritual or they are waiting for their turn to take holy dip. Summary and Conclusions Crowd turbulence is potentially life-threatening and experienced in hundreds of crowd-intensive events each year (Helbing et al., 2007). A proper knowledge of crowd behaviour is necessary to build a simulation tool so that it can aid in effective crowd control and management. This study tries to understand the eternal flow of humanity arriving at the ghat with the sole intention of taking holy dip. The nature of activities undertaken by the crowd creates obscure patterns of flow in a semi- confined space. The primary observation of video data indicated the multifaceted pedestrian behaviour, such as conflicting movements within single lane, creeping phenomenon, and platoon formation, seldom occurring in normal situations. Analogous to the fluid flow through porous medium, the pedestrians are assumed to navigate through the study section represented as a system of pores. Analysis of the arrival pattern of pedestrians into spatially separated pores is done. The results indicate that the arrival rate follows Poisson distribution at a bin width of less than 5 seconds. Also, the results showed a large variation of local densities as represented by occupancy. This variation is very important as safety in crowd is not determined by the average density but by the maximum occurring local density. Also, the duration of holy dip and inflow are found to be statistically significant in influencing the arrival rate of pedestrians into the pore. The main contribution of this paper to the existing literature on pedestrian flow is in understanding the microscopic pedestrian behaviour in large mass religious gatherings using real data as opposed to controlled experimental setups. The study also highlights the need to specify the bin width at which the arrivals can safely be assumed as Poisson while simulating pedestrian flows. It also gives evidence to support the need to understand variations in local densities rather than going for averaged density as risk in case of such huge gatherings can be analyzed by limiting values of parameters rather than averaged values. Specific to mass religious gatherings, especially in India, where people gather around to perform some spiritual activity like holy dip, the study brings forth the need to study the waiting behavior of pedestrians in a crowd. 15
The research on behavioral aspects of pedestrians, with specific consideration to high density crowds is still in its early stages. There is great scope in improving crowd safety by studying their dynamic behavior, especially at extreme density conditions. However, the proposed framework has its limitations in representing the behavior of individuals in a crowd. Therefore, there is a need to suitably modify this framework to bring forth the behavioral realism of crowd. REFERENCES 1. Arasan, V. T., & Dhivya, G. (2008, December). Measuring heterogeneous traffic density. In Proceedings of the international conference on sustainable urban transport and environment, World Academy of Science, Engineering and Technology, Bangkok, pp. 342-346. 2. Communicable disease alert and response for mass gatherings, World Health Organization WHO, 2008 3. Dridi, M. H. (2015). List of Parameters Influencing the Pedestrian Movement and Pedestrian Database. International Journal of Social Science Studies, 3(4). doi:10.11114/ijsss.v3i4.870 4. Dubey, S. K., Ponnu, B., & Arkatkar, S. S. (2012). Time Gap Modeling under Mixed Traffic Condition: A Statistical Analysis. Journal of Transportation Systems Engineering and Information Technology, 12(6), 72-84. doi:10.1016/s1570-6672(11)60233 5. Hariharan G., Aparna P.M., Verma A (2017). A review of studies on understanding crowd dynamics in the context of crowd safety in mass religious gatherings, International Journal of Disaster Risk Reduction, Volume 25, pp 82-91 6. Helbing, D., Johansson, A., & Al-Abideen, H. Z. (2007). Crowd turbulence: the physics of crowd disasters, arXiv: 0708.3339. 7. Highway capacity manual 2000: (2005). Washington, D.C.: Transportation Research Board. 8. Hossain M, Iqbal G A (1999) Vehicular headway distribution and free speed characteristics on two-lane two way highways of Bangladesh. J Inst Eng 80: pp. 77-80. 9. Illiyas, F. T., Mani, S. K., Pradeepkumar, A. P., & Mohan, K. (2013). Human stampedes during religious festivals: A comparative review of mass gathering emergencies in India. International Journal of Disaster Risk Reduction, 5, pp. 10-18 10. Johansson A, Helbing D, Al-Abideen HZ, Al-Bosta S (2008). From Crowd Dynamics to Crowd Safety: A Video-Based Analysis. Advances in Complex Systems 11 (04), pp. 497527. 11. Moussaïd, M., Helbing, D., & Theraulaz, G. (2011). How simple rules determine pedestrian behavior and crowd disasters. Proceedings of the National Academy of Sciences, 108(17), pp. 6884-6888. 12. Nair, R., H. S. Mahmassani, E. Miller-Hooks (2011) A porous flow approach to modeling heterogeneous traffic in disordered systems. Transportation Research Part B: Methodological, 45(9), pp. 1331 – 1345. 13. Rouphail, N., J. Hummer, J. Milazzo II, and P. Allen (1998) Capacity Analysis of Pedestrian and Bicycle Facilities: Recommended Procedures for the Pedestrians Chapter of the Highway Capacity Manual. Federal Highway Administration Report Number FHWA-RD16
98-107, Office of Safety & Research & Development, Federal Highway Administration, 6300 Georgetown Pike, McLean, VA 22101-2296 14. Shaha, J., Joshib, G. J., & Paridac, P. (2013). Behavioral Characteristics of Pedestrian Flow on Stairway at Railway Station. Procedia - Social and Behavioral Sciences. 104, pp. 688-697. Elsevier.doi: 10.1016/j.sbspro.2013.11.16 15. Ubboveja V S & Bhatia O (1993), Management of super-density pedestrian traffic along a street using psychological approach, Indian Roads Congress, pp. 64-72 16. Gulhare S., Verma, A., Chakroborty P., (2018) “Comparison of Pedestrian Data of Single File Movement Collected from Controlled Pedestrian Experiment and from Field in Mass Religious Gathering”, Collective Dynamics, 3, pp.1-14 Central Library, Forschungszentrum Jülich GmbH, Germany, DOI: 10.17815/CD.2018.16. 17. Johansson, F. (2013). Microscopic Modeling and Simulation of Pedestrian Traffic (Unpublished master's thesis), Linköping University, Sweden. 18. Bellomo, N., & Gibelli, L. (2015). Toward a mathematical theory of behavioral-social dynamics for pedestrian crowds. Mathematical Models and Methods in Applied Sciences, 25(13), 2417-2437. doi:10.1142/s0218202515400138
Research Highlights
Real field data was collected as a part of Kumbh Mela, mankind’s largest religious mass gathering
A high degree of complexity was observed in the movement of crowd
A porous flow approach is proposed to understand the dynamics of crowd at the Ghat region where the pilgrims take a holy dip
The microscopic behavior of pedestrians is studied using parameters such as pore occupancy, arrival rate of pedestrians, and duration of holy dip
17
PII: DOI: Reference:
S2212-4209(18)30509-0 https://doi.org/10.1016/j.ijdrr.2018.08.005 IJDRR961
To appear in: International Journal of Disaster Risk Reduction Received date: 21 April 2018 Revised date: 8 August 2018 Accepted date: 8 August 2018 Cite this article as: P S Karthika, P M Aparna and Ashish Verma, Understanding Crowd Dynamics at Ghat regions during World's Largest Mass Religious Gathering, Kumbh Mela, International Journal of Disaster Risk Reduction, https://doi.org/10.1016/j.ijdrr.2018.08.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Understanding Crowd Dynamics at Ghat regions during World’s Largest Mass Religious Gathering, Kumbh Mela
P S Karthikaa, P M Aparnab, Ashish Vermac* a
Research Scholar, Department of Civil Engineering, Indian Institute of Science (IISc), Bangalore - 560012, India Email: [email protected]
b
Project Associate, Department of Civil Engineering, Indian Institute of Science (IISc), Bangalore - 560012, India Email: [email protected]
c
Associate professor, Department of Civil Engineering and Robert Bosch Centre for Cyber Physical Systems, Indian Institute of Science (IISc), Bangalore-560012, Karnataka, India. Email: [email protected] * (Corresponding Author) Abstract In this paper a porous flow approach on a cul de sac is proposed to understand the dynamics of crowd at ghat regions (banks of the sacred river) in mass religious gatherings. Kumbh Mela, one of the mankind’s largest religious gathering encompassing almost all possible crowd scenarios, provides a unique opportunity to explore the crowd dynamics along all facets. Here, Cul-de-sac refers to the ghat region where people gather with the intention to take holy dip. The data used for this study was collected during Kumbh Mela held during 22nd April to 21st May 2016. Visual observations from the video data shows a high degree of complexity probably due to the nature of activities at the study location, e.g., lane formation, creeping behaviour etc. The proposed porous flow approach divides the entire study area into pores, and it is assumed that pilgrims traverse this network through interconnected vacant pores. The pedestrian data from video sequences (entry time, exit time, and flow) is extracted manually and time series analysis of pore occupancy is done to get an approximate measure of local density. Further, using Poisson regression analysis it was found that both the inflow and the duration of holy dip are significant factors in influencing the number of arrivals into the pore. Since behavioral aspects of a pedestrian is a significant governing factor of crowd dynamics, these microscopic parameters can be used to get a measure of criticality of the system in terms of crowd risk.
Keywords: Crowd dynamics, Porous flow, Occupancy, Arrival pattern of pedestrians, Kumbh Mela, India
1
Introduction A crowd is referred to as a group of heterogeneous people congregated or collected into a closed body without order, characterized by a common interest. World Health Organization [3] defines mass gatherings as “more than a specified number of persons at a specific location for a specific purpose for a defined period of time”. Although crowd dynamics has been extensively studied, there is still scope for investigating different behavioural aspects purely because uncertainty is inherent where humans are concerned. The challenges imposed by this uncertainty in the behaviour of the crowd translates into panic situations, resulting in large casualties. Developing economies are observed to be more prone to fatalities from crowd risk situations in such mass gatherings. Religious gatherings and pilgrimages have been venues for 79% of stampedes in India (Illiyas et al., 2013). In India, with its diversity in religion, language and culture, numerous religious festivals are celebrated every year resulting in large number of mass gatherings. A few of these include Kumbh Mela, Sabarimala pilgrimage, and Godavari Maha Pushkaram. Among these, Kumbh Mela is the mankind’s largest gathering, where an estimated 75-100 million people visit the event site in a span of one month. This could also be attributed to the fact that India is the second most populous country in the world. Considering all these, studying the crowd dynamics at mass religious gatherings is highly relevant and important to improve crowd safety. This study aims at understanding the crowd dynamics at ghat regions (river banks) in Kumbh Mela held in Ujjain during 22nd April to 21st May, 2016, popularly known as Simhasth-2016. Kumbh Mela is a mass Hindu pilgrimage held at four different places, namely Haridwar, Ujjain, Nasik, and Allahabad, every three years. Most of the earlier Kumbh Mela’s have been marred by events resulting in loss of lives and large number of casualties. The last Kumbh Mela held in Ujjain, during April-May 2016 witnessed a natural calamity resulting in 7 deaths. Similarly, crowd crushes have taken a toll of 36 lives in Kumbh 2013, 39 in Kumbh 2003, 50 in Kumbh 1986, and 800 in Kumbh 1954. These numbers are indicative of the sensitivity of the crowd in expediting the risk factors and thereby triggering stampedes. An extensive review of the literature on the various studies on crowd is beyond the scope of this paper. The authors would however, like to highlight a few studies which are relevant to the present work. As mentioned previously, there is a large body of work available in the area of crowd behaviour. In general, the pedestrian models are usually characterized according to the scale of the variables used in the model as microscopic, mesoscopic, and macroscopic. The macroscopic approaches associate pedestrian flow to the flow of fluids and gases, without explicitly modeling the individuals and their interaction. The microscopic models on the other hand focus on the individual entities and their interactions with other individuals and the environment. The 2
mesoscopic approaches model the pedestrian movements and their interaction through averaged out quantities, making them computationally more efficient than microscopic models (Johansson, F. 2013). A variant of this is the behavioral-social dynamics model proposed by Bellomo, N. et al.,(2015) where the pedestrians belong to one particular group (known as the “functional subsystem”) based on a variable called,”activity variable”. This is a part of the microscopic state of the pedestrian along with the position, and velocity. The interactions between the pedestrians are modeled through the transition probability density that changes the activity variable. Here, it is possible to account for the different emotional states of pedestrians based on the strategies adopted by the individual. A previous study on the crowd behavior at Kumbh Mela by Ubboveja et al., (1992) concentrated on the qualitative aspects of pedestrian traffic. It was found that a high level of potential risk existed during different timings at various locations in Kumbh Mela 1992. The author developed a simulation model to evaluate psychological behavior and introduced a parameter PRI (Psychological Rating Index) which is a numerical value for exhibiting the instant psychological potential risk levels at any location. One important behavioral characteristic identified is that the density is not the only criteria for the explanation of crowding behavior and crowd risk level. Rush and surge of people, accidents, natural or human induced hazards, rumors, competition of procurement, sudden change of entry/exit points, end-of-event exit or beginning-of-event surge are the sources of crowd disturbances and triggering factors of crowd crush, which were identified from the case studies (Illiyas et al., 2013). A similar study on Hajj devotees by Johansson et.al (2008) also points out that neither the density nor the speed or flow field are good measures of the criticality in the crowd. Another study conducted in Mina also highlights the lack of understanding about the characteristics and behavior of pedestrians in cases of high density crowd dynamics (Dridi, 2015). Hariharan et al., (2017) emphasized on the need to conduct studies on mass religious gatherings in an uncontrolled setup as the circumstances are very dynamic and different from a controlled experimental setup. For the safety of pilgrims in mass religious gatherings, to ensure an early response to any emergency situation/problem, or to predict an emergency situation/problem, a sophisticated and continuous monitoring system like an early warning system is very much required. Various experiments serving as input to mathematical model which can be formulated to calculate crowd risk index (CRI). The current state of the system coupled with simulations based on route choice algorithms will provide a feedback to the CRI and this value can possibly be used by event managers to manage crowd to increase crowd safety. All these studies have emphasized on the need to understand the crowd dynamics at high densities much more rigorously.However, literature consisting of studies to understand crowd dynamics using real field data at mass religious gatherings is sparse. Most of the studies on crowd behaviour is also concentrated on experimental data. The present work intends to focus on 3
one particular type of gathering, a mass religious gathering known as “Kumbh Mela”, where people don't hesitate to barter their personal safety for a chance to be a part of the gathering. . The following are the objectives of the study. ● To understand the crowd dynamics at ghat regions by studying the different patterns of movements exhibited by the pedestrians and to conclude possible explanation for these visual observations ● Develop a conceptual framework for modeling the observed flow patterns with the help of analogous system using the insights derived from general observations ● Understanding the relation between macroscopic parameters of pedestrian flow ● Interpreting the microscopic behavior of pedestrians using parameters such as pore occupancy, arrival rate of pedestrians, and duration of holy dip The paper is organized as follows. The upcoming section gives an overview of the data collected and the importance of the location at which the data is collected. Based on the observations, goals defining the study have been identified in the next section. The following section describes the conceptual framework. Analysis and results are discussed in the next section, and the final section highlights the merits and shortcomings of the study. Data Collection The data used in this study was collected in Kumbh Mela 2016 in which an estimated 75 million people participated during a span of 1 month. The field work was done for 30 days, from 22nd April 2016 to 21st May 2016. Video recordings were taken at different locations including corridors, river banks and intersections. From the video recordings, the study section was chosen such that the people could be observed with clarity as to how they conduct themselves at ghat regions. The pedestrian data used in this study was collected by video capturing the pedestrian flow at Ram ghat, considered to be the most auspicious location for holy dip, on 9th May 2016, also known as “Shahi Snan” day. This particular day is chosen for the analysis since it is marked with highest inflow during the whole event. The next section provides a brief overview of the location considered for the analysis to get an understanding of the feel of the crowd and their associated activities. Cul-de-sac Generally, Cul-de-sac refers to a street or passage closed at one end. Here, it means a nonthrough space providing access for people who intend to take holy dip. The event can be described as a gathering of people for a common purpose by some prearrangement. Huge numbers of pilgrim’s flock to the ghat regions with a belief to cleanse themselves of their sins by taking holy dip in the sacred river. Unique crowd dynamics is thus created, when the entire crowd moves towards the river to take holy dip, at the Ghat area. Since most of these pilgrims come in groups, they spend considerable amount of time at the banks for every one of them to conclude their activities. It is like a system that contains a number of companion clusters where 4
people arrive, remain and leave together. The participants show a great variation from the most privileged sadhus (holy men) to the common people from rural areas. On special days of holy dip, the crowd density at ghats become extremely high. The data has a high degree of complexity due to the nature of activities at the study location. Here, the microscopic behavior of pedestrian movement is of great utility in gaining an understanding of the macroscopic state of the system. This is especially true in the studied situation where the change in trajectory of a single pedestrian has the ability to change the flow dynamics at least locally. Also, the space utilization of the crowd when observed at a macro level is highly uneven. This could be ascertained by modeling the changes in local densities. By studying the different patterns of movements exhibited by pedestrians in a crowd, it will be possible to understand the crowd dynamics and thereby provide more insights on the critical parameters to be used in simulation. Snapshots of the study section is shown in fig 1. A number of interesting points about crowd dynamics were visually observed from the data and could be noted by plain visual observation of the video data as summarized. ● Unlike vehicular traffic, multi directional pedestrian movement is observed in a single lane ● Crowd continues to move even at higher densities. This same phenomenon is observed by Johansson et al., (2008) in Mina ● Pedestrians tend to move in groups similar to platoons, the group sizes varying from 2 to approximately 8. The different groups interact within themselves and with others ● Pedestrians weave themselves into nearly continuous lanes despite the high densities and move seamlessly among each other without experiencing friction ● Backtracking behavior in face of jammed conditions (e.g. due to barricading by police) ● Creeping behavior similar to that in vehicular flow is observed by the acceptance of very small gaps through which sometimes they appear to squeeze through by creating or expanding gaps. Ubboveja et al., (1993) have found that the minimum acceptable gap is as low as 15 cm under controlled movement conditions in a line ● Multiple leaders in a single line itself which results in rather splitting up of formed lanes or merging between two lanes
5
Figure 1 Screenshots of ghat areas at Kumbh Mela-2016
Theoretical Framework The conventional way of modeling the parameters in a heterogeneous vehicular traffic is to adopt the same methodology as in homogeneous lane-based traffic with some minor adjustments which are expected to account for the heterogeneity. This results in serious under estimation of the difference in flow patterns occurring as a result of variation in vehicular dimensions, speed and lane indiscipline. In a non- lane-based traffic, be it vehicular or pedestrian, headways and average density are not suitable measures of modeling traffic flow. In the present context, with multi directional, haphazard sort of pedestrian movement and without defined pathways for walking, the same established parameters for defining the distinct patterns produced by pedestrians cannot be adopted. Pedestrian study conducted at railway stations by (Shaha et al., 2013) tries to understand the fluctuations in pedestrian flow depending on the arrival and departure of trains. This study, though not in the context of mass religious gatherings have similarities in the pedestrian behavior in Kumbh Mela as even here people carry luggage, they travel in groups, and they are goaloriented. The study shows different speed – flow trends at different size staircases. Nair et.al (2012) has proposed a novel porous flow approach for traffic flow modeling, where pores are defined as spaces between vehicles and roadside. This paper adopts a similar porous flow approach for modeling pedestrian behavior at cul-de-sac. Broadly, this approach is derived from the flow of fluid through a porous medium. In the study of porous materials, the portion of space not occupied by the soil mass, excluding all those soil pockets or vesicles bounded on all sides by soil particles is considered as pore space. Analogous to the fluid flow through porous medium, the pedestrians are assumed to navigate through the study section represented as a system of pores. Individuals, though being distinct entities, 6
defining boundaries for each individual and their respective groups are difficult as the amount of space occupied by each segment would be different. They actively seek a free path through the crowd instead of being repelled by their neighbors (Moussaid et al., 2011). Instead of defining pores on similar lines, it is our intention to consider the entire study area as partitioned into small pores. At any instant of time, the interest is in the fraction of pores that are empty, as this would give an idea of how pedestrian movements are possible even at high densities if minuscule spaces are distributed throughout the study section creating a network of pathways. For this reason, pores are classified as follows (refer Fig. 2): ▪
Passive pores: pores that are occupied by stationary pedestrians and hence are not free for movement at an instant of time
▪
Active pores: pores that are free for pedestrians to occupy or readily available for access at an instant of time
Figure 2 Concept diagram showing set of paths at any instant of time between origin and destination
A particular feature of the pedestrian flow in the ghat regions is the distinction between stationary and moving pedestrians. People come to the ghat regions with the aim of taking holy dip. Predominantly, they come in groups, complete their intended activity, wait for all the other members of their group, and then leave together. This forces them to spend some time in the study area with negligible relative movement. The distinctive feature of these activities at ghat regions is the one that allows us to differentiate the system of pores into active pores and passive pores. These are two distinct states through which the state of a pore can be identified. Also, at any instant of time, a passive pore can change to an active pore and vice versa. An important point to be noted is that unlike conventional study, here there is no single origin and destination, but origin and destination are spread out over a length. It is more of an areaorigin (AO) to area-destination (AD). Thus, the problem is defined as modeling the pedestrian flow between an area-origin to area-destination through a system of active pores forming a set of 7
paths. Here, path is defined as a set of connected active pores at an instant of time and the paths are themselves dynamic. At any instant of time, there would be a set of pathways, subject to changes. The interaction between stationary and moving pedestrians results in creation of new paths or an existing path becoming redundant. Therefore, for any individual, who wishes to travel from AO to AD has a set of paths at his departure time from origin. A different kind of user equilibrium exists between these dynamic paths as follows. ● At user equilibrium, all users try to minimize their perceived travel time ● Thus, every used path would have the same perceived travel time ● Users will shift to alternate paths (either created or existing) only if they feel that their travel times are bound to increase if they stay on their path. This can happen if their path is obstructed by some stationary pedestrians or in case of heavy conflicting flow. ● Also, the unused paths are perceived to take longer travel times. These paths will again become active only if either of the previous conditions is met. Modeling the pedestrian flow through these dynamic paths would be a realistic representation of the patterns created while the crowd moves through the study area. As pointed out by Dridi (2015), “Psychology of every individual moving along a street with a specific goal, suddenly changes realizing any obstruction to his goal, influencing his behavior tremendously thereby raising the potential risk level of a group to behave as a crowd.” The following section presents data extraction and results of the study.
Data Extraction The pedestrian data from video sequences obtained from CCTV cameras is extracted manually for duration of 30 minutes. The extracted data include time of entry and time of exit from a pore, inflow into the entire study section (refer fig 3), and the duration of holy dip. The limiting dimensions of the pore are chosen such that at least a single pedestrian is a part of the frame enclosed by the pore boundaries at any instant of time. The approximated area of pore is 0.45 sq. m. This is similar to the minimum area required for a standing pedestrian. As per HCM standards for queuing area (Exhibit 11-9 Queuing area LOS, HCM 2000) required per pedestrian for LOSD is 0.3-0.6 m2/pedestrian.
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Figure 3 Schematic diagram of study section
Number of pedestrian arrivals per unit time data is collected for 30 minutes for a number of pores. This exercise is carried out for another time interval also. The main objective of such an extensive analysis is to understand the spatial and temporal variability of pedestrian arrivals. The duration of holy dip per pedestrian and the incoming and outgoing flow values per unit time are also collected. Heterogeneous traffic in non-lane-based conditions is usually explained by the analysis of headways. Most of these studies propose headways as either exponential distributed or negative binomial distributed (Hossain M et.al, 1999). The same is usually applied to pedestrian traffic also. The next section presents the macroscopic fundamental diagrams obtained from the extracted data. The effect of bin width in deciding the distribution of pedestrian data is presented in the subsequent section. Analysis and Results Figure 4 shows the macroscopic fundamental diagrams at the approach to ghat (referred to as Ram ghat). It could be seen that average speed ranges from 0.8m/s to 1.5m/sec, whereas density varies from 0.8-3.5 ped/m2. The flow values range from 24 ped/m/min to 39 ped/m/min. Unlike the usual flow-density relationships, as density increases the flow remains a relatively constant value. It is also possible that the group behaviour could be a reason for this deviation in the flowdensity relation. A comparison of the flow conditions using experimental data and the field data collected in mass religious gatherings indicates significant differences indicating that the people participating in mass religious gatherings have a common mindset in terms of motivation (Gulhare et al., 2018). Since a uniform relation couldn’t be obtained for the various macroscopic parameters, the data was split into two based on a cut-off value corresponding to the mean flow of 30 ped/m/min. The resulting two flow regimes (fig. 4c) with respect to flow- density relationship show a higher fit in terms of R2 instead of the combined flow conditions (fig. 4d). However, it is important to note that there is no significant variation in the range over which the speed varies for different flow values.
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Figure 4a, 4b: Speed-flow and speed-density diagrams
Fig 4c Flow-density diagram for two regimes
Figure 4d Flow-density diagram for single regime Figure 4 Fundamental flow diagrams at approach to Ram Ghat
Time gaps between successive pedestrians entering a prescribed pore are considered for the analysis of arrival pattern. It is clear from literature that different distributions are proposed for modeling vehicular time-gap by different authors for the same flow range (Dubey et.al, 2012). 10
However, there are only a few studies on modeling the arrival pattern of pedestrians. As a first step, there was a need to ascertain if the pedestrian arrivals into a subset of the area could also be safely assumed as Poisson distributed and to investigate its dependency on the bin width (notated as t). To this purpose, the exercise of fitting Poisson distribution for different bin widths is carried out, and the results are demonstrated using figure 5. The time interval was reduced from t of 60 seconds to a t of 1 second. It could be noted that as the t decreases, the arrivals seem to follow Poisson distribution. The same results were observed when the analysis was done for other pores also. An interesting observation is that dual arrivals show a peaking over single arrivals at all bin widths except for t-5sec. This could be due to two reasons. The first one being the group behavior and the second one being the conflicting arrivals at the same time. It is not possible to identify the groups in detail due to the concentrated movement at the ghat. So, an argument presented to explain this observation is that the 2 arrivals at the same instant of time is the effect of people competing for the same available gap. Therefore, the two arrivals have a higher probability of coming from conflicting flow rather than from the same group, as members within a group have less chance of competing.
A rr iv al fr e q u e n c y o f p e d
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e st ri a n s
Number of pedestrian arrivals Figure 5 Variation in the arrival distribution as a function of the bin size chosen
The effect of pore size and shape variation on the arrival pattern of pedestrians was also investigated. For this purpose, the size of the pore was gradually increased to a point when manually noting the arrival rate of pedestrians were difficult owing to the simultaneous arrival of more than 3 pedestrians into the pore. The shape of pore was also varied to understand the possible variations in arrival pattern. The main conclusion to be drawn from this analysis is that beyond a fixed pore dimension of 0.65 sq. m, it cannot not be considered as a pore in this study. This is because the aim was here to model the gaps that pedestrians are willing to accept, and large pores don’t occur at high densities. Also, in such low flow conditions, there is no need to understand the pedestrian dynamics as people can move freely and complete their activities. In such contexts, the theory of gap acceptance itself is not relevant. The average amount of time that an individual occupies a space has special significance in the ghat region. This is because, holy dip is the primary purpose of visit for majority of the people visiting the Kumbh Mela and hence, the need to understand the amount of time they spend waiting to get a chance or waiting for their group members to complete the ritual. This can also be considered as a kind of area occupancy, where it can be used to relate to macroscopic parameters of flow, namely, density. Here, pore occupancy is defined as the number of pedestrians occupying a pore at any instant of time. Alternately, it could be defined as the percent of time a pore is occupied by a pedestrian relative to the total analysis period. The second definition of area occupancy proposed by Arasan et.al (2008) for vehicular flow is adopted in pedestrian scenario. Either way, the term occupancy could be considered as some measure of local density. Therefore, understanding the variation in occupancy over time is studied in detail. The temporal variation in occupancy for pores placed at different locations in the study area is as shown in figure 6. It could be seen that the highest occupancy is 3 persons/second.
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Figure 6 Occupancy trend plot
It can be observed that at P3 (pore nearer to the ghat), people occupy the same spot for a longer period of time compared to other locations. This may be attributed to the fact that the location 3 is nearer to the ghat and people spend considerable amount of their time at the ghat as they have to wait for all the members of their group to complete the holy dip. The other two locations are along the entry to the ghat and therefore show the corresponding changes in their occupancy patterns. In such locations, rather than modeling the average density over a length it would be better to model the range of concentrated densities at different spatial points in the study area. This would enable us to understand the distribution of local densities and how to effectively tackle these densities. The pedestrian behaviour at the ghat region with pedestrians waiting for their turn to take holy dip amidst the predominantly stagnant crowd is similar to the passenger behavior at railway stations. Dwell time models have been used to study the dwell time of trains (i.e. the time available for passengers to board/alight). It has been generally observed that dwell times can be optimized considering the passenger volume, train design, percentage of standing-through passengers, luggage etc. Here, instead of optimizing the holy dip duration, the effect of duration of holy dip and the inflow into the study area on the number of arrivals of pedestrians into the sample pore is analyzed. This is done using Poisson regression. Arrivals into a pore is assumed to be independent. The count variable, the number of arrivals into the sample pore in a given time interval is assumed to follow a Poisson process whose parameters are decided by the average duration of holy dip in that time interval and the inflow into the study area. Here, yi- the number of arrivals into the pore, ‘i’ (
)
13
The expected number of arrivals per time period is specified log-linearly as
(
)
where,
Two models were estimated, one with inflow alone as the explanatory variable (model b) and the other with both pedestrian inflow and average duration of holy dip as explanatory variables (model a). The estimated parameters are tabulated below. Table 1 Results of Poisson regression
Model a (Unrestricted model) variables Intercept Pedestrian inflow Holy dip duration
Estimate (signf codes) 1.4375 (***) 0.0535 (***) -0.087 (**)
Model b (Restricted model)
Std error
Z-value
0.134
10.720
0.005
9.942
0.0521
0.0278
-3.139
-0.0911
Elasticity
Estimate (signf codes)
Std error
1.319 (***) 0.049 (***)
0.12 4 0.00 5
-
-
Z-value 10.628 9.565 -
LL
-130.84
-137.18
AIC
267.69
278.36
Rp2
0.349
0.288
It could be noted that both the inflow and the duration of holy dip are significant factors in influencing the number of arrivals into the pore. The model (a) shows that as the duration of holy dip increases, the number of arrivals into pore decreases. Comparing the two models, it could be said that the model (a) gives a better fit to the data. The AIC value is lower for model (a) compared to model (b). Also, the Rp2 value of model (a) is greater than model (b). A common test for assessing the two models is the likelihood ratio test. Here, the Null hypothesis, H0: ??hdurn = 0 i.e. Pedestrian arrivals does not vary with the duration of holy dip 14
Elasticity
0.0481
Alternate hypothesis, H1: ??hdurn ≠0 The number of restrictions, R=1. For 1 degree of freedom, at 95% confidence level is 3.84. ??????=12.67> . Therefore, there is sufficient evidence to reject the null hypothesis. It could be concluded that the unrestricted model (Model a) is better than the restricted model (Model b). The final model is therefore, given by
As the duration of holy dip per individual increases, the pores near to the ghat gets blocked resulting in a further decrease in the number of arrivals. This block could be the result of two reasons: either they are waiting for their group members to complete the ritual or they are waiting for their turn to take holy dip. Summary and Conclusions Crowd turbulence is potentially life-threatening and experienced in hundreds of crowd-intensive events each year (Helbing et al., 2007). A proper knowledge of crowd behaviour is necessary to build a simulation tool so that it can aid in effective crowd control and management. This study tries to understand the eternal flow of humanity arriving at the ghat with the sole intention of taking holy dip. The nature of activities undertaken by the crowd creates obscure patterns of flow in a semi- confined space. The primary observation of video data indicated the multifaceted pedestrian behaviour, such as conflicting movements within single lane, creeping phenomenon, and platoon formation, seldom occurring in normal situations. Analogous to the fluid flow through porous medium, the pedestrians are assumed to navigate through the study section represented as a system of pores. Analysis of the arrival pattern of pedestrians into spatially separated pores is done. The results indicate that the arrival rate follows Poisson distribution at a bin width of less than 5 seconds. Also, the results showed a large variation of local densities as represented by occupancy. This variation is very important as safety in crowd is not determined by the average density but by the maximum occurring local density. Also, the duration of holy dip and inflow are found to be statistically significant in influencing the arrival rate of pedestrians into the pore. The main contribution of this paper to the existing literature on pedestrian flow is in understanding the microscopic pedestrian behaviour in large mass religious gatherings using real data as opposed to controlled experimental setups. The study also highlights the need to specify the bin width at which the arrivals can safely be assumed as Poisson while simulating pedestrian flows. It also gives evidence to support the need to understand variations in local densities rather than going for averaged density as risk in case of such huge gatherings can be analyzed by limiting values of parameters rather than averaged values. Specific to mass religious gatherings, especially in India, where people gather around to perform some spiritual activity like holy dip, the study brings forth the need to study the waiting behavior of pedestrians in a crowd. 15
The research on behavioral aspects of pedestrians, with specific consideration to high density crowds is still in its early stages. There is great scope in improving crowd safety by studying their dynamic behavior, especially at extreme density conditions. However, the proposed framework has its limitations in representing the behavior of individuals in a crowd. Therefore, there is a need to suitably modify this framework to bring forth the behavioral realism of crowd. REFERENCES 1. Arasan, V. T., & Dhivya, G. (2008, December). Measuring heterogeneous traffic density. In Proceedings of the international conference on sustainable urban transport and environment, World Academy of Science, Engineering and Technology, Bangkok, pp. 342-346. 2. Communicable disease alert and response for mass gatherings, World Health Organization WHO, 2008 3. Dridi, M. H. (2015). List of Parameters Influencing the Pedestrian Movement and Pedestrian Database. International Journal of Social Science Studies, 3(4). doi:10.11114/ijsss.v3i4.870 4. Dubey, S. K., Ponnu, B., & Arkatkar, S. S. (2012). Time Gap Modeling under Mixed Traffic Condition: A Statistical Analysis. Journal of Transportation Systems Engineering and Information Technology, 12(6), 72-84. doi:10.1016/s1570-6672(11)60233 5. Hariharan G., Aparna P.M., Verma A (2017). A review of studies on understanding crowd dynamics in the context of crowd safety in mass religious gatherings, International Journal of Disaster Risk Reduction, Volume 25, pp 82-91 6. Helbing, D., Johansson, A., & Al-Abideen, H. Z. (2007). Crowd turbulence: the physics of crowd disasters, arXiv: 0708.3339. 7. Highway capacity manual 2000: (2005). Washington, D.C.: Transportation Research Board. 8. Hossain M, Iqbal G A (1999) Vehicular headway distribution and free speed characteristics on two-lane two way highways of Bangladesh. J Inst Eng 80: pp. 77-80. 9. Illiyas, F. T., Mani, S. K., Pradeepkumar, A. P., & Mohan, K. (2013). Human stampedes during religious festivals: A comparative review of mass gathering emergencies in India. International Journal of Disaster Risk Reduction, 5, pp. 10-18 10. Johansson A, Helbing D, Al-Abideen HZ, Al-Bosta S (2008). From Crowd Dynamics to Crowd Safety: A Video-Based Analysis. Advances in Complex Systems 11 (04), pp. 497527. 11. Moussaïd, M., Helbing, D., & Theraulaz, G. (2011). How simple rules determine pedestrian behavior and crowd disasters. Proceedings of the National Academy of Sciences, 108(17), pp. 6884-6888. 12. Nair, R., H. S. Mahmassani, E. Miller-Hooks (2011) A porous flow approach to modeling heterogeneous traffic in disordered systems. Transportation Research Part B: Methodological, 45(9), pp. 1331 – 1345. 13. Rouphail, N., J. Hummer, J. Milazzo II, and P. Allen (1998) Capacity Analysis of Pedestrian and Bicycle Facilities: Recommended Procedures for the Pedestrians Chapter of the Highway Capacity Manual. Federal Highway Administration Report Number FHWA-RD16
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Research Highlights
Real field data was collected as a part of Kumbh Mela, mankind’s largest religious mass gathering
A high degree of complexity was observed in the movement of crowd
A porous flow approach is proposed to understand the dynamics of crowd at the Ghat region where the pilgrims take a holy dip
The microscopic behavior of pedestrians is studied using parameters such as pore occupancy, arrival rate of pedestrians, and duration of holy dip
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