Multi-Agent Management of Crowds to Avoid Stampedes in Long Queues

Thesis submitted in partial fulfillment

of the requirements for the degree of

MS by Research

in

Computer Science Engineering

by

Sindhu Kolli

200802019sindhu.kolliug08@students.iiit.ac.in

Center for Data Engineering

International Institute of Information Technology

Hyderabad - 500 032, INDIA

July 2014

Copyright c© Sindhu Kolli, 2014

All Rights Reserved

International Institute of Information Technology

Hyderabad, India

CERTIFICATE

It is certified that the work contained in this thesis, titled “Multi-Agent Management of Crowds to

Avoid Stampedes in Long Queues” by Sindhu Kolli, has been carried out under my supervision and is

not submitted elsewhere for a degree.

Date Adviser: Prof. Kamalakar Karlapalem

To My Family

Acknowledgments

I would like to take this opportunity to sincerely thank my guide Prof. Kamalakar Karlapalem, for

his immense support and constant guidance, without which this thesis would not have been possible.

Working under his guidance has been a great learning experience. I thank him for encouraging and

helping me understand the subject better.

I would like to thank the institute for providing a great atmosphere and support to carry out my

research. I would like to thank my friends Anusha Balusu, Anusha Konduri, Archita, Susmitha and

Vasudha for their support and encouragement through out my B.Tech and specially Anisha, Apeksha

and Shipra for spending some of their valuable time discussing and reviewingmy work. I thank them

for all the motivation.

Finally, I would like to thank my family for being supportive at every step of my life. I am grateful

to my father, who always believed in me, who always made time to discuss my education, for his

inspiration and motivation. I thank my mother, for all her love and affection. And my little sister, for

being a great friend and, for her lovely and thoughtful advices.

v

Abstract

In places of reverence, wherein large crowds gather to have small duration of time for individual

solace, there is a long queue of people waiting for their turn. A typical example of this scenario is a

temple wherein each person visiting the temple, would want to spend a small amount of time to offer

prayers in front of a deity. During auspicious occasions there will be hundreds of thousands or more

anxious people queuing at the temple wanting to pray. Some other examples would be long shopping

queues and queuing at ticketing counters for large crowd gathering events (like sports, music concerts).

A crowd management force (that is police or security) at such events, are present to monitor the crowd

and prevent any crowd disasters. Yet, there have been cases of stampedes with significant loss of life

and trauma in such occasions because of lack of efficiency in the management of crowds. This presents

us with a scenario where a multi-agent based system can be used to help improve the efficiency of crowd

management at temples.

In this thesis, we develop a multi-agent based system for simulating the scenario of crowding in long

queues at temples. We focus on how introducing external agents in this scenario would help manage

the crowd better. First, we introduce MAMAC (Multi-Agent MAnagement of Crowd), a set of robotic

agents that can move at a height above the queue, (i) to provide direction and monitor the crowds,

and (iii) to avoid occurrences of stampedes. We then focus on increasingthe efficiency of the robotic

agents. A method of movement has been developed that can be used by these robotic agents to ensure

smooth flow of the crowd. Finally, we present a solution that uses only the required number of robotic

agents that can manage the crowd to achieve a stampede free flow. We evaluate the efficiency of crowd

management by conducting various experiments on the multi-agent simulation showing the results of

robotic-agents avoiding the possibility of stampedes to occur.

vi

Contents

Chapter Page

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 MAMAC (Multi-Agent MAnagement of Crowd) . . . . . . . . . . . . . . . . . .. . 2

1.1.1 Robotic Agents for Crowd Management . . . . . . . . . . . . . . . . . . . . .21.1.2 A Method of Movement for Robotic Agents . . . . . . . . . . . . . . . . . . . 21.1.3 Required Number of Robotic Agents for Crowd Management . . . . . . .. . 3

1.2 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Crowd Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Multi-agent based crowd simulation systems . . . . . . . . . . . . . . . . . . 62.2 Crowd Disasters: Crowd Management . . . . . . . . . . . . . . . . . . . . . .. . . . 7

2.2.1 Crowd Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Crowd Management at Temples . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 MAMAC: Multi-Agent System for Management of Crowd at Temples. . . . . . . . . . . . 103.1 Description of scenario of crowding at Temples . . . . . . . . . . . . . . . .. . . . . 103.2 Multi-Agent Simulation Framework for Queuing at Temples . . . . . . . . . . . .. . 123.3 Simulation Model for MAMAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.3.1 Human Agents Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3.1.1 Heterogeneous Human Agents . . . . . . . . . . . . . . . . . . . . 133.3.1.2 Force Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3.1.3 Human Agents Parameter Update . . . . . . . . . . . . . . . . . . . 15

3.3.2 Crowd Managing Robotic Agents Model . . . . . . . . . . . . . . . . . . . . 15

4 Management of Crowd in Long Queues using Crowd Managing Agents. . . . . . . . . . . . 164.1 States of the Queue at Temples and Calculation of Prayer time (δ) . . . . . . . . . . . 194.2 Method of Movement for Crowd Managing Agents . . . . . . . . . . . . . . .. . . . 234.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27

5 An Extended Method of Movement for Crowd Managing Agents. . . . . . . . . . . . . . . 295.1 A Different Perspective of determining Various States of Queuing . . .. . . . . . . . 305.2 Extended Method of Movement for Robotic Agents . . . . . . . . . . . . . . .. . . . 315.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

vii

viii CONTENTS

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38

6 Required Number of Crowd Managing Robotic Agents. . . . . . . . . . . . . . . . . . . . 396.1 Using a Required Number of Crowd Managing Agents . . . . . . . . . . . . .. . . . 396.2 Determining the required number of robots . . . . . . . . . . . . . . . . . . . . .. . 416.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45

7 Conclusions and Future Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

List of Figures

Figure Page

3.1 Robots monitoring the crowd using their thermal sensor’s view range . . .. . . . . . . 113.2 A robot shows Red signal, when it determines high density in its detection range that

leads to a state of congestion in the queue. . . . . . . . . . . . . . . . . . . . . . . .. 113.3 Forces Affecting the Human AgentHi within its influence range of radiusr . . . . . . 14

4.1 Fruin’s Levels of Service (FLOS) [28]: Flow rate (Number of peopleper width [inmeters], per time [in minutes]) for each level is, FLOS A - less than 23 people per meterper min, FLOS B - between 23-33 people per meter per min, FLOS C - between 33-49people per meter per min, FLOS D - between 49-66 people per meter per min, FLOS E- between 66-82 people per meter per min, and LOS F - highly variable. With increasein the level, there is increase in the density of crowd. . . . . . . . . . . . . . . . .. . 17

4.2 Causes of injury/death during a stampede . . . . . . . . . . . . . . . . . . . . .. . . 184.3 Various states of queuing at temples. . . . . . . . . . . . . . . . . . . . . . . . .. . . 204.4 Force(F) exerted by people increases asλ increases andµ decreases. It is maximum

whenλ is maximum andµ is minimum. It is minimum whenλ is minimum andµ ismaximum. The dark gray shaded region represents congestion leading to stampede. . . 21

4.5 Various States of Queuing: (a) Free Flow, (b) Constant Flow, (c) Congestion Flow, and(d) Stampede. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.6 Robot are numbered starting from the main temple arena to the queue entrance. R0 isplaced at the entrance of main temple arena andRn−1 is placed at the entrance of thequeue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.7 Series of actions of robots to reduce congestion. . . . . . . . . . . . . . .. . . . . . . 264.8 The state of the queue would be determined as congestion flow, but not all the areas of

the queue are congested. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27

5.1 Various states of a queue between two robotsRk andRk−1 . . . . . . . . . . . . . . . 305.2 A simulation state of queuing at temples with crowd managing agents using the extended

method of movement for managing the crowd. . . . . . . . . . . . . . . . . . . . . . .335.3 The robotsR0, R1, R2, R3 andR4 are static and show Green. In this state people in the

main temple arena are allowed forδmax time to offer their prayers. . . . . . . . . . . . 335.4 This shows that the main temple arena is full and the robotR0 shows Red for aδmax

time. As there is increase in the flow rate (people entering per minute), people enteringin this state are accumulated at robotR0 until they are allowed into the main templearena for prayers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 34

ix

x LIST OF FIGURES

5.5 Since people are accumulating at the robotR0, the robotR1 moves towards the maintemple arena to control the crowd accumulating. Once the robotR1 detects congestionin an area, it stops and shows Red stopping people from accumulating further. . . . . . 34

5.6 The main temple arena is now vacant that the robotR0 shows Green allowing people(who were earlier accumulating atR0) to enter until the main temple arena is full. TherobotR1 is Red as the flow rate at robotR0 is not high to reduce the congestion aheadof R1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.7 When the flow rate increases at the entrance, the rate of people passing the robotR4 ishigher than the rate of people passing the robotR3, and people entering the queue pushthemselves exerting forces on people already in the queue. In this case, the robotR4

shows Red stopping people from passing through, there by reducing theforces experi-enced by people that have already passedR4 until the flow rate atR3 is higher than theflow rate atR4 and congestion is reduced. . . . . . . . . . . . . . . . . . . . . . . . . 35

5.8 This shows a situation where there is free flow of people from robotsR4 to R1 andR1

is moving towardsR0 to detect any congested areas, as there are people accumulatingatR0. AndR0 is showing Red as the main temple arena is not vacant. . . . . . . . . . 35

5.9 The graphs of flow rate (λ) vs simulation time (t) for the robotsR0, R1, R2, R3 andR4 using the method of movement (Algorithm 1). The robotR0 shows Red forδ timewhen the main temple arena is occupied. The Red and Green dots on a graph show thechanges in the signal of the corresponding robot. The prayer timeδ for which the robotR0 shows Red, is calculated using the in-flow rateR1.λ, out-flow rateR0.µ, δmin andδmax. Hereδmin=10s andδmax=50s. . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.10 The graphs of flow rate (λ) vs simulation time (t) for the robotsR0, R1, R2, R3 andR4

using the method of movement (Algorithm 1) for about 550 simulation time steps. Thisgraph shows that the robotR2 remained idle during this simulation run. Hereδmin=10sandδmax=50s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

6.1 Considering the queue flowing from the robotRk+1 to the robotRk−1. (i) The robotRk

determined two congested areas with very high densitiesDk(l1, l2) andDk(l1, l2). (ii)The robotRk does not detect any high density regions. . . . . . . . . . . . . . . . . . 41

6.2 Two robotsR1 andR0 are initially placed at the entrance of the queue and in front ofthe main temple arena respectively.R0 shows Green as the main temple arena is vacantandR1 shows Green as there is yet no accumulation atR0. . . . . . . . . . . . . . . . 42

6.3 RobotR0 shows Red as the main temple arena is occupied andR1 starts moving towardsR0 where people have started accumulating in front of the main temple arena, to detectany congestion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6.4 OnceR1 detects congestion, it stops and shows Red. This is when it calls for a newrobot (R2) that is placed at the entrance. . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.5 The number of people entering the queue increased suddenly at the entrance and therobotR2 detects a congestion state based on the flow rate determined. It moves towardsR1 and shows Red when it detects any congested area. A new robot is not called as therobotR2 detects only one region that is highly congested. . . . . . . . . . . . . . . . . 43

6.6 The robotR2 is removed as the robotR1 does not detect any congested areas andR1

takes the previous position ofR2. The robotR1 shows green as there is not yet anyaccumulation at the robotR0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

LIST OF FIGURES xi

6.7 The graphs of flow rate (λ) vs simulation time (t′) for the robotsR0, R1 andR2 usingthe method described in Algorithm 2 for moving and using the method described inAlgorithm 3 to add or remove a robot. Here, the robotR2 is called at a later stage. . . . 44

6.8 The graphs of flow rate (λ) vs simulation time (t′) for the entrance and robotsR0 andR1 from t′=0s to t′=70s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.9 The graphs of flow rate (λ) vs simulation time (t′) for the entrance and robotsR0, R1

andR2 from t′=60s to t′=130s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.10 The graphs of flow rate (λ) vs simulation time (t′) for the entrance and robotsR0, R1

andR2 from t′=120s to t′=220s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486.11 The graphs of flow rate (λ) vs simulation time (t′) for the entrance and robotsR0 and

R1 from t′=220s to t′=290s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.12 The graphs of flow rate (λ) for the robotsR0,R1 andR2 vs. simulation time (t′) of about

300 simulation time steps. The robotR2 is added to the track at time stept′=81s. TherobotR1 is removed at time stept′=214s there by monitoring the area from entrance ofthe queue to the main temple arena. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.13 These graphs of prayer time (δ) determined vs. simulation time (t) of about 300 simu-lation time steps, compares the scenario in which no crowd managing agents areusedto manage the queue, with the scenario in which crowd managing agents are used tomonitor the queue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

List of Tables

Table Page

4.1 The range of values for flow rates, average space taken by a pedestrian (ped) and densitydefined for Fruin’s Levels of Service [4,28]while queuing. . . . . . . .. . . . . . . . 18

4.2 The range of values for flow rates, average space taken by a pedestrian (ped) and densitydefined for different states of queuing at temples. . . . . . . . . . . . . . . .. . . . . 19

4.3 The situations that occur at temples for different states of queuing. . .. . . . . . . . . 204.4 Prayer timeδ determined using in-flow and out-flow rates. Here,δmin=10s andδmax=50s. 27

5.1 The states of an individual queue betweenRk andRk−1 are determined using the in-flowrate (λk) and out-flow rate (µk) of people. . . . . . . . . . . . . . . . . . . . . . . . . 30

6.1 Scenario I: Using crowd management agents to monitor the crowd. . . . . .. . . . . . 516.2 Scenario II: Using NO crowd management agents. . . . . . . . . . . . . . .. . . . . . 516.3 Scenario I: Using crowd management agents to monitor the crowd. . . . . .. . . . . . 536.4 Scenario II: Using NO crowd management agents. . . . . . . . . . . . . . .. . . . . . 536.5 Scenario I: Using crowd management agents to monitor the crowd. . . . . .. . . . . . 536.6 Scenario II: Using NO crowd management agents. . . . . . . . . . . . . . .. . . . . . 53

xii

Chapter 1

Introduction

Everyday hundreds of events are held across the world which attract acrowd. ‘A crowd’ has multiple

vague definitions [15,51,53,57,59,80,86], more often described around the concept of a crowd beinga

large gathering of people. In order to successfully manage a crowd at a particular event, it is important

to distinguish different types of crowd [13]. The key criteria characterizing a crowd include: size, den-

sity, time, collectivity and novelty. Momboisse (1967) [55] distinguishes fourtypes of crowd: Casual,

Conventional, Expressive and Aggressive. We focus on ‘conventional’ crowds, which are the ones with

members gathered for a specific purpose or to observe a specific event,that is with crowd members who

share common interests. One such scenario that is referred to in this thesis is, a long queue of pedes-

trians (at temples) flowing in a specific direction sharing a common goal (offering prayers in front of a

deity).

In the scenario crowding at temples, long queues usually occur when people come to pray to a deity

in first come first serve manner. When very few people visit the temple, there is no waiting with free

flow of people and each person can spend substantial amount of time in front of the deity to pray. But

on auspicious occasions, even though there is restriction on amount of time aperson spends in front of

a deity, the queue is highly dense with many people people wanting to pray, that(i) the queue moves

very slowly, (ii) people get tired (some of them might be fasting) and (iii) severe congestion could lead

to stampede due to over enthusiastic people pushing themselves with force into the queue. Forces, as

a result of being both propagated and additive in the direction in which they are exerted, are location

specific [43, 44]. That is, most injuries occur either at the front of a crowd, where the forces are most

concentrated, or in the center of a crowd, where forces from individuals pushing off a wall combine with

forces from individuals pushing from the back [27]. By the time the crowdmanagement force (police

or security) at temples notices the stampede, the situation would have already gotten worse. Therefore,

it is important to manage the crowd in long queues by detecting and reducing congestion as soon as it

occurs. This motivated us to introduce external agents which help to efficiently manage the crowd and

reduce congestion in this scenario.

1

1.1 MAMAC (Multi-Agent MAnagement of Crowd)

Our solution is to deploy MAMAC, a multi-agent management system for managingcrowds in long

queues at temples. The model used for the simulation of crowds is based on asocial force model

by Helbing [38]. With the motivation of utilizing robotic agents to enhance the crowd management

techniques, this system was built in three steps: (i) a simulation system was developed to generate

crowds in long queues and a set of robotic agents are introduced for crowd management, (ii) a method

of movement for the robotic agents is presented in order to manage the flow ofthe crowd, and finally (iii)

a solution is provided to be able to use only a required number of robotic agents for crowd management

in long queues. The main contributions of this dissertation are as follows:

1.1.1 Robotic Agents for Crowd Management

Management of crowd in long queues is an important issue that is addressed in this dissertation. In

general, the crowd management force (police or security) at temples is notcapable of detecting con-

gested areas or any disturbances in the crowd as soon as they occurs.By the time, the situation of a

stampede comes into notice, it would have already gotten worse that the stampede continues to occur

prior to the instructions of crowd management force. This motivated us to introduce robots moving at a

height above the queue that are capable of: (i) monitoring the crowd usingthermal imaging sensors, (ii)

estimating the congestion levels and detecting disturbances as soon as they occur in the crowd, and (iii)

taking proactive measures to space out the people in the queue to reduce congestion.

A multi-agent based simulation has been developed to simulate the crowd in long queues at tem-

ples. The robots capable of managing the crowd are introduced into this simulation as crowd managing

robotic-agents. These robotic agents are placed at equal distances from each other on a track located at

a height above the queue. They continuously move in their assigned division on the track to identify the

areas of congestion in the crowd. In this dissertation, we do not delve into the robot design, construction

and thermal image processing aspects to determine congestion levels. The input to our multi-agent man-

agement system is the current location of robots on track and the congestion levels as determined by the

robots. The system will move the robots and get them to take actions to reducecongestion. The actions

taken by a robot is communicated to the remaining robots managing the queue enlightening them with

the change in the environment, based on which the actions taken by other robots might differ.

1.1.2 A Method of Movement for Robotic Agents

When robotic agents are placed at equal distances from each other, thequeue is divided in to several

areas, that is the area of queue between any two robotic agents is assigned to one of these. The robotic

agents move continuously in their assigned area of the queue to monitor and manage the crowd, which

might drain the battery of the robots quickly in a real time scenario. This is not necessary, unless there

2

is congestion in that particular area that has been assigned to the robotic agent. That is when there

are very few people passing across a robotic agent, there would not beany congestion for the robotic

agent to detect and hence it can be static until there is increase in the rate offlow of people. In order

to achieve this and improve efficiency of these robotic agents, a method of movement is presented,

which moves the robotic agents when necessary. In this method, the long queue is divided into several

individual queues, each for which a robotic agent is assigned. That isthe area of the queue assigned to

a robotic agent for it to monitor is treated as a separate queue. The robotic agents manage their assigned

individual queues and perform actions depending on the congestion levels and states of the individual

queue, using the people flow rate values determined by its adjacent robotic agents. Thus, collectively

achieving a stampede free flow of the crowd in the long queue.

1.1.3 Required Number of Robotic Agents for Crowd Management

Say, every temple provides some number of robots for crowd management. The above methods place

all the robots available, at equal distances from each other above the queue to monitor the crowd, that is,

the number of robots used are the same through all different states of the queue and equal to the number

of available robots. But, not all the robots available are needed to manage the crowd during all states of

the queue. For example, when the entrance gates of the queue are just opened, that is when people have

just started to enter the queue, the actions performed by all robots (except for the robot that is present

at the entrance) are not effective. Hence, an algorithm has been developed to add or remove robots in

the multi-agent system, such that, only the number of robotic agents required for managing the crowd

(in a particular state of the queue) are utilized. This algorithm allows a robotic agent to be added to the

queue (that is, when the congestion in the crowd cannot be reduced with those robotic agents that are

already managing the queue) or removed from the queue (that is, when there is a robotic-agent that is

managing the part of queue which is free of congestion). These required number of robotic agents use

the algorithm of the method of movement. We also show that the number of robotic agents (as per the

algorithm) used to manage the queue at a given time is equal to the required number, by ensuring that

there is no congestion in the queue at any given point of simulation time.

1.2 Overview of the thesis

This thesis is organized as follows:

In Chapter 2, we present the work related to crowd simulation models and understanding the crowd

behavior.

In Chapter 3, we describe our multi-agent management system. The force model used to simulate

the crowd, human agent model and crowd managing robotic agent model.

In Chapter 4, we present a method of movement for the crowd managing robots and determine

different states of queuing.

3

In Chapter 5, the method of movement used earlier and determining the states ofthe queue are

extended to achieve efficiency in the management.

In Chapter 6, an algorithm is described which adds or removes robots to use only the required number

of robotic agents for crowd management. In all the chapters above we present results justifying the

algorithms used.

In Chapter 7, we summarize the contributions of the thesis.

4

Chapter 2

Related Work

Many theories have been developed on crowd behaviors [25,69,71,72,85], suggesting that people in

crowds often behave in a common and a collective manner, that is, crowd members are succumbed to the

social influence of wider crowd [59]. Although social influence is a powerful force, crowd membership

is not homogeneous, it comprises of individuals, each of whose actions may differ to such social influ-

ence. Crowds can be merely physical with the members behaving as individuals while in the presence of

others [19,71]. In recent years, analyzing crowd behaviors has been an active area of research. Various

models [38,73,93] have been developed and simulated to study the crowd dynamics.

2.1 Crowd Simulation

Crowd simulation involves developing models and simulating the behavior of crowd and their move-

ment to match real-world crowding scenarios. Simulations of crowd behaviors serve different purposes:

training in crowd management [84, 89], architecture and urban planning [23, 52, 56, 79], formulating

evacuation and rescue strategies for disaster scenarios [21,22,54,58,68]. In general, there are two types

of models for simulating crowd movement: (i) macroscopic models, for the behavior of the crowd as

a whole and (ii) microscopic models, for the behavior, decisions and interactions of individuals within

the crowd [16, 49, 62–64, 67, 94–96]. A drawback of macroscopic models is that the features such as

physical abilities, direction of movement, and positioning of an individual in thecrowd cannot be con-

sidered [10, 91]. A broad classification of microscopic models developedfor crowd simulations are as

follows:

1. Rule-based models:Most well known of the rule-based models is the ’Boids’ model proposed by

Reynolds (1987) [73,74]. It likens the movement of crowd to the movementof herds of animals.

The model uses a ’flocking algorithm’ to describe animal and crowd movementcomprising the

elements of: separation, alignment, cohesion, and avoidance [73,74,77]. In particular, the flock of

birds when flying, each bird keeps as near to its neighbors as possible avoiding collisions among

5

themselves and with obstacles moving in a direction guided by a homing instinct. These models

have been criticized for lacking realism, flocking of birds is similar to an autonomous herd with

pre-programmed actions and behaviors, whereas a realistic human crowdconsists of individuals

with varied decision making abilities. By determining an individuals choice of movement ac-

cording to the direction and proximity of other individuals, other factors which may influence the

crowd behaviors have been overlooked [67].

2. Social force models: Many researchers have considered the analogy between fluid particles

movement and crowd movement. Most cited example of fluid dynamics is a behavioral force

model of individual pedestrian dynamics, typically used in panic simulations proposed by Hel-

bing and colleagues [24, 32–40, 42]. This model describes the collective behavior of particles,

wherein each particle is self-driven, has a destination and is prepared tomove at a given velocity

to reach the destination [65]. This model involves various forces of an individual : (i) acceleration

- the velocity of each individual varies over time in the attempt to reach optimum speed, (ii) re-

pulsion - there is a repulsive force from other individuals and obstacles, (iii) attraction - there can

be a force of attraction towards the destination [38]. These models have been criticized for failing

to capture some crowd behaviors such as herding behavior, multi-directional flow, and very high

density crowd distributions [61,82].

3. Cellullar automata models: Cellular automata models or matrix based systems also involve

forces on an individual, but the environment is treated as discrete in space and time. The environ-

ment is divided into a uniform grid of discrete cells which represent free areas, or areas occupied

by individuals, or obstacles [17, 92, 93]. Each individual occupies aparticular cell or position on

the grid and moves from cell to cell according to a set of rules which definewhether the individual

can occupy a particular cell or not [90]. These models are criticized thatthey limit the individuals

behavior to grid-based movement with an assumption of static environment, negating the reality

of a dynamic environment [66,67,82].

2.1.1 Multi-agent based crowd simulation systems

Multi-agent based systems are in which an environment is modeled as a collection of intelligent,

autonomous, decision-making entities called agents which interact within a virtual environment. Multi-

agent based systems are more suitable for simulating situations involving heterogeneous agents and

dynamic environment [12, 78, 91]. These systems have recently been applied to crowd simulation ap-

plications. Models described above can be employed in these systems. Eachindividual in these models

is considered as an agent with varying attributes of gender, age, body size, mobility, walking speed and

other capabilities. This enables the agent-based simulations to capture uniquesituation of each indi-

vidual within a given environment representing the heterogeneous nature of crowds [20, 88]. Despite

the clear advantage of these models, human behaviors are complex emergent phenomena, which are

difficult to be captured by computers as mathematical equations and hence themodels are still thought

6

to be lacking psychological elements [63]. Agent-based systems are beingwidely applied to social sim-

ulations (known as ABSS - Agent Based Social Simulation systems) to understand the complex social

phenomena, hypothesize and predict system behavior [1,18,50].

Tomoki et al. [31] developed a simulation method of crowd behavior which uses multi-agent frame-

work on cellular automata model. Henein et al. [43] adapt Kirchners cellularautomata model [45],

with forces for modeling local forces. Pan et al. [63], presented a multi-agent based framework for the

simulation of human and social behaviors during emergency evacuations. In [47, 87] , the authors have

described an agent- based simulation of pedestrian dynamics. In [75] the authors have explored the

application of Belief-Desire-Interaction architecture [14], to pedestrianmodeling. Osaragi [60] has de-

scribed a model describing pedestrian behavior using the concept of mental stress. Lovas [52], presents

a model for simulation of pedestrians flowing in a queue. In [76], authors improve the pedestrian dy-

namics by applying lattice-gas concepts to the social forces model. These simulation models differ from

the scenario of queuing at temples as they do not take into account that widthof the queue is limited.

In [11], an agent-based model to simulate pedestrian crowd in a corridor.This model accounts to the

limited width of the queue flow, but unlike our temple queuing scenario, pedestrians have multiple goals.

In this thesis, we develop a force model to simulate queuing of pedestrians attemples. They move

in the same direction to reach their common destination while the width of the queue is limited with an

entrance and an exit.

2.2 Crowd Disasters: Crowd Management

When there is a large crowd gathering at an event or for an occasion, anything unusual in the crowd,

like mass impulsive behavior, or a situation of panic with poor venue design and poor crowd manage-

ment leads to crowd disasters resulting in wider scale of life loss and injury [48]. In this thesis, we

address the possibility of occurrence of stampedes in long queues. Some severe stampedes in long

queues that took place in the past are:

• Phil-Sports Stadium Stampede:

In February 2006, about 30,000 people gathered outside the Phil-sports stadium, Philippines to

participate in the first anniversary episode of a popular television game show. It is when the event

organizers started handing out tickets, people in the queue started trying toget ahead of the queue

and people at the entrance started pushing themselves into the queue. The security was asked to

close the entrance gates, but the situation grew worse resulting in a stampedekilling 78 people

and around 400 people got injured [7].

• The Hajj Pilgrimage:

7

Hajj pilgrimage has a history of crowd disasters. In 1998, 2001, 2004, and 2006, people got

crushed and trampled to death as a result of sheer force of crowd pressure and massive crowd

surge caused by excessive number of pilgrims. The 2006 stampede killed around 360 people and

around 300 people got injured [9].

• Sabarimala Stampede:

In January 2011, at Sabarimala, a famous Hindu pilgrimage center in India,a human stampede

took place which killed 106 pilgrims and injured more than 100 [8].

Hence, avoiding such crowd disasters (stampedes), is an important issueto be addressed.

2.2.1 Crowd Management

The terms crowd management and crowd control are used interchangeably, but it is operationally

important to acknowledge the distinction between crowd management and crowd control, to enable

more appropriate prevention for an event, along with more suitable action or intervention during the

event [13, 81]. According to Fruin (1993) [27], crowd management concerns with the facilitation of

both the activities and crowd members at an event, to not only ensure that thecrowd are able to safely

enjoy the event which they came to observe or to be part of, but also to encourage the crowd to behave

in the desired manner. For example, ticket sales, seating, parking, noise control, public announcements,

concession stands and communication are all aspects of crowd management.And crowd control, on

the other hand, concerns the actions taken to organize the crowd once they begin to exhibit undesirable

behaviors, such as disorder. More forceful measures then need to be taken to quickly bring the crowd

back under control, such as limiting access, controlling admissions and makingarrests. If management

is well-planned and well-organized, it should be possible to prevent or quickly resolve the majority of

problems arising at crowd events [13]. Hence, crowd management is preferable to crowd control.

Many researchers have studied various agent based crowd simulationsto understand the behavior of

crowd in situation of panic. Many applications have been built which include education, training and hu-

man behavior analysis to provide crowd management solutions or architectural solutions for emergency

evacuations. In [13], authors have presented a new architecture combining their MACES (Multi-Agent

Communication for Evacuation Simulation) with PMFServ (Performance Moderator Functions) sys-

tems, in which the agents communicate to understand the environment, which helpsin the evacuation.

In [29], authors present a collision avoidance approach based on theconcept of velocity obstacles (VO)

introduced by [26] and in [70], a collision avoidance approach which combines psychological and geo-

metrical rules with social forces model is presented along with global path planning. In long queues, the

environment is a direct simple path, communication amongst thousands of agents is not feasible, and

collisions are not considered as the motion of all agents is not random, but inthe same direction (peo-

ple push themselves ahead exerting high forces) in such scenarios. Joel et al. [46], studied the effects

of crowd dynamics introducing external autonomous agents into crowds. These agents are effective at

8

improving the crowd flow by inducing an attractive social force. In the scenario of long queues, intro-

ducing external agents in between the crowd is not effective due to limitationsin width of the queue.

Hence, in our dissertation, we present MAMAC, a system of robots whichmove overhead the queue in

order to monitor or manage the crowd in the queue.

2.2.2 Crowd Management at Temples

In order to ensure safe environment for the crowd, the most important factor is to plan for the crowd

management, develop intervention and crowd control strategies. At any massive crowd gathering, there

is always a crowd management force (police or security guards) to control the behaviors of crowd that

impact public safety. Every event should be independently assessed to determine the plan for crowd

management that will effectively support and provide public safety. To control the crowd at temples,

crowd management force follows a basic crowd management planning whichincludes the following

steps:

(i) Controlling the Entry into the Queue:

Some members of the crowd management force are located at the entrance and exit to control the

flow of people entering and exiting the queue, which is highly necessary to handle the crowd.

(ii) Monitoring the Crowd Behavior:

The crowd management force has to continuously monitor the crowd to identifyany nonadaptive

behavior, that is behavior that can cause disasters.

(iii) Communication:

Once they identify any disturbances (congestion or stampede) in the crowd, the member of the man-

agement force that identified this disturbance has to communicate it to the other members of the force.

This will help the crowd management force at the en- trance to minimize the flow orthe crowd manage-

ment force at the exit to maximize the flow or stop crowd movement to create space.

(iv) Controlling the Crowd:

Once the information is communicated, the crowd management force is expectedto control the part

of the crowd where the disturbance occurred.

In order to observe the crowd and detect the disturbances occurring inany part of the queue, we

may require large number of members in the crowd management force team. To carry out all the

above mentioned steps efficiently, there has to be a better communication between the members of the

crowd management force. But, with higher the number of members in the team, it ismore difficult for

an efficient communication and with limited members, the crowd management force team will not be

able to monitor the whole crowd. Hence, introducing MAMAC, will help improve efficiency in crowd

management. The robots overhead, can observe the crowd, communicate among themselves and pass

instructions to the people in an efficient manner than the members of a crowd management force team.

9

Chapter 3

MAMAC: Multi-Agent System for Management of

Crowd at Temples

Given the predominant increase in events occurring everyday that attract large gatherings of people,

there are potential safety issues associated with it. Hence, there is a need for efficient crowd management

at any crowd gathering events. One such scenario which has high influence is the large scale movement

of people visiting temples (pilgrims) during pilgrimages.

3.1 Description of scenario of crowding at Temples

At a temple, the environmental changes (temple spatial and human behavioralcharacteristics) are

highly governed by seasonality, limited time and limited space. The most common elements of people

visiting the temples are motivation, destination and journey. People travel alongthe long queue in the

same direction in a hurry to reach their destination (that is, the main temple arena), where they can offer

their prayers to the deity for some allotted time (which is referred to as prayer timeδ in this dissertation).

When few people who can fit in the main temple arena are offering their prayers, there are people wait-

ing in the queue for their turn. Regardless of the people waiting in the queue,there is a large number of

people visiting the temple during auspicious occasions. That is, a continuousrate of people entering the

queue, pushing themselves exerting forces on people who already entered the queue causing a stampede.

As a solution to the scenario of crowding (queuing) at temples, we introduceMAMAC, a system

of robots, wherein each robot is individually called a crowd managing robot (agent), that is built to

be able to monitor the crowd. The main purpose of these robots is that they have faster and better

communication, and we would require smaller number of robots to monitor the crowd than the number

of human members we require as a part of crowd management force (policeor security). A track is

located at a height above and along the path of the queue for these crowdmanaging robots to move.

10

Figure 3.1Robots monitoring the crowd using their thermal sensor’s view range

Figure 3.2A robot shows Red signal, when it determines high density in its detection range that leadsto a state of congestion in the queue.

11

Each robot has a thermal imaging sensor attached to it, to count the number ofpeople in its detection

range [6]. A thermal imaging sensor, if located at a heightht, covers a rectangular area (detection range)

with dimensions of lengthlt and widthwt. Thus, the track on which the robots move, is located at a

minimum height from ground level, such that the width of a thermal sensor’s detection range covers the

width of the queue, and the length of this detection range would vary with varying the height at which

the track is located (see Figure 3.1). A thermal imaging sensor can count thenumber of individuals in

its range, by detecting the heat emitted by their bodies regardless of different light levels.1 This count

is used to calculate the flow rate of the people at each robot and density of the crowd in the detection

range to determine the various states of the queue. Each robot has a signal light attached to it, that shows

either Green or Red, depending on if it should allow people to pass through, or should stop them from

entering a congested area, respectively (see Figure 3.2). Each robot can wirelessly communicate (i) any

changes detected by robot in its environment (people count and congested areas), (ii) information about

the current position of robot on the track, etc, to the other robots positioned on the track. Each robot,

upon receiving inputs from other robots, processes the information about the congestion levels, to move

and to act accordingly (whether to stop[red] or allow[green] people to pass through, as described in

Chapter 4).

3.2 Multi-Agent Simulation Framework for Queuing at Temples

The simulation framework of the multi-agent crowd management system (MAMAC) for temples is

a continuous time simulation built using MASON, a multi-agent simulation toolkit. This framework

consists of the following modules:

• Map Generator Module: This module generates a map in which the human agents are allowed

to queue. It has an entrance, exit and the main temple arena where the humanagents are allowed

to offer their prayers in front of a deity. The spatial information about themap is given to this

map generator module.

• Human Agent Module: This module generates heterogeneous human agents (Section 3.3.1.1)

using a Force Model (Section 3.3.1.2) and a Parameter Update (Section 3.3.1.3) to update the

parameters of the generated human agents.

• Crowd Managing Agent Module: This module generates crowd managing robotic agents (Sec-

tion 3.3.2) and consists of methods to update their parameters.

• Crowd Management Module: This module includes the method of movement and crowd man-

aging techniques (explained in Chapter 4) used by the crowd managing agents.

1Thermal sensors are preferred to cameras, as they do not need complex image processing algorithms. Since the mainobjective of these robots is to detect the congestion levels, we do not use cameras to prevent from taking any identifiableimages of the individuals visiting the temple.

12

• Temple GUI Module: A visualization module has been implemented which initiates the human

agents and crowd managing agents in to a map generated by the Map Generator Module. In every

cycle of a simulation run, the human agents parameters, and crowd managing agents’ positions

are updated accordingly and the crowd managing agents act based on thechanges determined in

the environment.

3.3 Simulation Model for MAMAC

3.3.1 Human Agents Model

3.3.1.1 Heterogeneous Human Agents

Each human agent has parameters which differs them from the other humanagents. Anith human

agentHi enters the queue at a timeti with an initial position~Ii(Ixi , Iyi ). A human agentHi occupies

a circular space of radiusri and has massmi which is directly proportional to the square of its radius

(r2i ). It has an initial velocity~ui (with which the human agent enters the queue), an initial or maximum

possible acceleration~amaxi (with which the human agent moves when there are no forces acting) and

a desired acceleration~adesi (with which the human agent actually moves after evaluating forces acting

on the agent). Each human agent has a circular range of influence of radius ′r′ which determines the

human agents present in this range that have an affect on the movement ofthe current human agent. A

boolean propertyInjuredi is assigned to each agent to determine if the human agent is injured. All

human agents have the prayer timeδ, to offer their prayers to the deity when inside the main temple

arena.

3.3.1.2 Force Model

The force model used is based on the continuous force model by Helbing. The map of the environ-

ment is a continuous two dimensional grid with path of the queue and walls (queue fencing) on either

side of the queue. This model includes three kinds of forces (i) the forcewith which humans push

themselves into the queue, (ii) the forces being exerted by other humans and(iii) the forces experienced

due to the presence of walls (see Figure 3.3).

The total force acting on a human agentHi is defined by the vector~Fi,

~Fi = ~F desi +

∑

i 6=j

~Fij + ~Fwi (3.1)

where,

13

Figure 3.3Forces Affecting the Human AgentHi within its influence range of radiusr

~F desi , is the force vector with which the agent is willing to move,

~F desi = mi.~a

desi (3.2)

~Fij , is equal to the component of force vector~Fj acting in the direction of the unit vector from the center

of the agentHj to the center of the agentHi,

~Fij =

(~Fj . ~bij~bij . ~bij

) ~bij , if | ~bij | < r

0 , otherwise

(3.3)

~bij , is the direction vector fromHj toHi,

~bij = (xj − xi)i+ (yj − yi)j (3.4)

~Fwi , is the force exerted by the walls on the human agentHi,

~Fwi =

(Kw

d) ~Wi , if d > r

0 , otherwise

(3.5)

Kw is a constant which is set to ensure appropriate force range,d is the perpendicular distance from the

human agent to the wall,r is the influence range of the agent,~Wi is the shortest unit vector from wall to

the agentHi.

14

3.3.1.3 Human Agents Parameter Update

Each human agentHi updates its parameters after a MASON simulation time step. Let this beτH .

The position of agent at timet is given by ~loci(t),

~loci(t) = ~loci(t− τH) + ~veli(t− τH) ∗ τH +1

2∗ ~ai(t− τH) ∗ τH ∗ τH (3.6)

where,

~veli(t), is the velocity of the human agentHi at timet,

~veli(t) = ~veli(t− τH) + ~ai(t− τH) ∗ τH (3.7)

~ai(t), is the acceleration of the human agentHi at timet,

~ai(t) =~Fi(t)

mi(3.8)

and,

~ai(0) = ~amaxi (3.9)

~veli(0) = ~ui (3.10)

~loci(0) = ~Ii (3.11)

~amaxi , ~ui, ~Ii are initial/maximum acceleration, initial velocity and initial position vectors of the human

agentHi respectively.Injuredi is set if the acceleration~ai(t) exceeds the maximum acceleration~amaxi

at any timet. The prayer timeδ is determined by the crowd managing agents.

3.3.2 Crowd Managing Robotic Agents Model

A crowd managing robotic agent (CMA)Rk has a rectangular detection range with widthw and

lengthl, and the track is located at a heighth. The robots are numbered such that the queue flows from

robotsRk toR0 and the robotRk−1 is referred as the robot previous toRk and the robotRk+1 is referred

as the robot next toRk. Each CMA has a propertysignalk that defines the color of the signal attached

to the robot and is set to either Red or Green. Letpeoplecount, (PCk) be the number of people present

in the current detection range ofRk, that can be used to determine the density (Dk) of the crowd in the

detection range.

Dk =PCk

w ∗ l(3.12)

The parametersPCk andDk are updated after every simulation time step (τH ), so that the densities are

determined whenever the human agents’ parameters are updated.

In the coming chapters we discuss the method of movement for these crowd managing agents and

other steps to manage the crowd of human agents in a long queue achieving a stampede free flow of

people.

15

Chapter 4

Management of Crowd in Long Queues using

Crowd Managing Agents

At temples, the occurrence of stampedes is due to the continuous rate of people entering the queue.

Hence, managing the crowd in a long queue would mean to manage the rate of flow of people in the

queue. The rate of flow of people (orFlow rate) is defined as the number of people flowing through the

queue per unit width of the queue per unit time. Level of Service (LOS) [3], is a concept of measure

used to determine and analyze the traffic flow. Fruin (1971) [28], developed an LOS standard for pedes-

trian walkways, queues and stairs. For the scenario of long queues, Fruins notion of Level of Service

(FLOF), defines six levels of pedestrian flow rate from level A - level F (see Figure 4.1). Table 4.1 shows

the flow rate, the average space taken by a pedestrian [4] and density (number of pedestrians per unit

area = 1/(average space)), defined for each level of service while queuing. With the increase in the flow

rate, there is increase in the density of the crowd, which increases congestion in the queue leading to the

main causes of injuries or deaths during a stampede [2] (see Figure 4.2), which are: (i)Compressive

Asphyxia: a person might experience extreme pressure causing lack of intake of oxygen leading to his

coma or death, (ii)Trampling: a person might lose his balance and stumble, which when followed by

trampling leads to a stampede.

The various states of queuing depend on the flow rates of the people (pedestrians), the average space

taken by a person and the density of crowd. An average space a person occupies while standing is said

to be 2 square feet, that is 0.186 square meters. And since the maximum average space occupied by

a person in FLOS (F) while queuing is 0.19 square meters, a person may getto occupy space lesser

than the average space he needs while standing. That is, in FLOS (F), humans experience extreme

forces acting on them, leading to causes of stampedes. In [41], Helbing and Mukerjhi have summarized

an expert report on Love Parade Disaster [5] by Still [83], which related the density of crowd to the

state of flow of people. When the density are increased up to 2-3 pedestrians per square meter, there

is an acceptable constant flow rate of people, with space available for crowd movement. And up to a

16

Figure 4.1Fruin’s Levels of Service (FLOS) [28]: Flow rate (Number of people per width [in meters],per time [in minutes]) for each level is, FLOS A - less than 23 people per meter per min, FLOS B -between 23-33 people per meter per min, FLOS C - between 33-49 people per meter per min, FLOS D -between 49-66 people per meter per min, FLOS E - between 66-82 people per meter per min, and LOSF - highly variable. With increase in the level, there is increase in the density ofcrowd.

17

Figure 4.2Causes of injury/death during a stampede

Fruin’s Flow rate Average Space taken DensityLevel of Service (in ped/m/min) (in m2/ped) (in ped/m2)

A ≤ 23 ≥ 1.21 ≤ 0.82B 23 - 33 1.21 - 0.93 0.82 - 1.08C 33 - 49 0.93 - 0.65 1.08 - 1.54D 49 - 66 0.65 - 0.28 1.54 - 3.57E 66-82 0.28 - 0.19 3.57 - 5.26F variable ≤ 0.19 ≥ 5.26

Table 4.1 The range of values for flow rates, average space taken by a pedestrian (ped) and densitydefined for Fruin’s Levels of Service [4,28]while queuing.

18

States of Flow Rate Average Space taken DensityQueuing (in ped/m/min) (in m2/ped) (in ped/m2)

(i) Free Flow ≤ 49 ≥ 0.65 ≤ 1.54(ii) Constant Flow 49 - 66 0.65 - 0.28 1.54 - 3.57

(iii) Congestion Flow 66 - 82 0.28 - 0.19 3.57 - 5.26(iv) Stampede ≥ 82 (variable) ≤ 0.19 ≥ 5.26

Table 4.2 The range of values for flow rates, average space taken by a pedestrian (ped) and densitydefined for different states of queuing at temples.

crowd density less than 2 pedestrians per square meter, there is a free flow with people moving at their

maximum possible speeds. When the crowd density increases up to 4-5 pedestrians per square meter,

the situation is likely to build up congestion implying a risk for the occurrence of stampede. When

there are increased densities upto 6 (or more) pedestrians per square meter, there is high risk of shock

waves with people getting injured and crushed. Based on the flow rates defined by Fruin’s Levels of

Service while queuing (see Table 4.1) and Still’s analysis on crowd densities, four different states of

queuing are defined for the scenario of crowd management at temples: (i)Free flow (FLOS (A-C)),

(ii) Constant flow (FLOS (D)), (iii) Congestion flow (FLOS (E)) and (iv)Stampede (FLOS (F), see Ta-

ble 4.2). According to Hall [30], a person has regions around him known as intimate space (of radius

= 0.46 m and space = 0.67 sq.m) and personal space (> 0.67 sq.m) and he shows discomfort if this

space is intruded by other individuals. This explains that a person feels uncomfortable in a queue, as

his personal space is always intruded. And in the states of constant flowand congestion flow, his inti-

mate space is occupied which leads to anger and anxiety displayed by a person while moving in a queue.

4.1 States of the Queue at Temples and Calculation of Prayer time (δ)

At temples, the states of queuing vary depending not only on the rate of people entering the queue

(in-flow rateλ), but also on the rate at which people are exiting the queue (out-flow rateµ). The relation

between the in-flow rate (λ) and the out-flow rate (µ) for different states of queuing at temples is shown

in Figure 4.3 and the situation at temples in these states is explained in Table 4.3. The force experienced

by people in all these states are different. When the in-flow rate (λ) is increasing while the out-flow rate

(µ) is decreasing, the force (F ) exerted on agents increases, and the force exerted on people in the queue

decreases whenλ is decreasing whileµ is increasing (see Figure 4.4). The various states of simulation

of human agents queuing at temples are shown in the Figure 4.5.

The time allotted for people to spend (offering their prayers) inside the main temple arena (prayer

time δ), depends on the state of the queue determined. Thus, the prayer timeδ can be determined using

the in-flow (λ) and out-flow (µ) rates of a queue. Letδmax be the maximum possible amount of time

people can be allowed to stay in the main temple arena andδmin be the least (minimum) amount of time

19

Figure 4.3Various states of queuing at temples.

States of Queuing Relation betweenλ and µ Situation at Temples(i) Free Flow λ < µ When a very few people are visiting the tem-

ple, there would be no waiting, people tend tomove freely and can spend substantial amountof time in front of the deity to pray.

(ii) Constant Flow λ ≈ µ When there is gradual increase in flow rate,people tend to move slow, waiting time in-creases and any sort of congestion is likely toget initiated.

(iii) Congestion Flow λ > µ If flow rate of people leaving the queue is nothigher than the flow rate of people enteringthe queue, it causes congestion and crowd be-comes agitated exerting forces on each other.

(iv) Stampede λ >> µ The state of congestion flow when continuesto be in the same state, this might lead to astampede.

Table 4.3The situations that occur at temples for different states of queuing.

20

Figure 4.4Force(F) exerted by people increases asλ increases andµ decreases. It is maximum whenλis maximum andµ is minimum. It is minimum whenλ is minimum andµ is maximum. The dark grayshaded region represents congestion leading to stampede.

21

Figure 4.5 Various States of Queuing: (a) Free Flow, (b) Constant Flow, (c) Congestion Flow, and (d)Stampede.

22

that can allotted for people to offer their prayers.δmax andδmin are usually fixed for a temple and so in

a simulation run. When only few people are visiting the temple, there is a free flowin the queue, that is

people can be allowed to spend substantial amount of time inside the main temple arena (in front of a

deity) and thus, the prayer timeδ is set toδmax. And when the queue is highly congested, sinceδ cannot

be made negligible, it is set to the minimum time allottedδmin, so that people can offer their prayers.

The flow rate calculated at the entrance, that is, the number of people entering the queue per width (w,

width of the queue) per time step (τR) is the in-flow rate (λ) of the queue and the flow rate calculated

at the exit, that is, the number of people exiting the queue per width per time step isthe out-flow rate

(µ) of the queue. The time stepτR is equal to the calculated prayer timeδ, so that the flow rate values

are updated whenever a new set of people walk into the main temple arena. The prayer time (δ) cannot

exceed the maximum prayer time (δmax) and should be greater than the minimum prayer time (δmin).

Hence,

δ(λ, µ, δmin, δmax) = minimum{δmin +µ

λδmin , δmax} (4.1)

Here,λ andµ are the in-flow and out-flow rates of the queue. This equation shows that when there is

free flow, that is when the out-flow rate is greater than the in-flow rate (µ ¿λ), δ is high, but, does not

exceed the maximum alloted timeδmax. Even when there is congestion, that is when in-flow rate is

higher than the out-flow rate (λ ¿µ), δ is low, but greater than minimum possible timeδmin.

4.2 Method of Movement for Crowd Managing Agents

Let L be the length of the queue from the main temple arena to the entrance and letn be the num-

ber of crowd managing agents available for monitoring the crowd. The queue is now divided inton

divisions, with each division equal to the length ofLn

. The robotR0 is fixed at the main temple arena,

which shows Green allowing people inside the main temple arena until the arena isvacant. Once, the

main temple arena is occupied, the robotR0 shows Red for the determinedδ (prayer) time. With one

robot placed at the main temple arena, all the remaining robots can be placed along the whole queue till

the entrance at equal distances from each other (see Figure 4.6). A robotRk while moving, covers the

area between its adjacent robots, that is, it has its extreme positions set to thecurrent positions of the

robotsRk+1 andRk−1. The robotRn−1 that is positioned at the entrance of the queue monitors the area

from the queue entrance to the robotRn−2. Once the robots (crowd managing agents) are placed at their

respective divisions, a simulation thread is started which runs continuouslycalling a control function

for the robotsR1 toRn−1, which implements the method of movement and actions for these robots (see

Algorithm 1).

The robots move continuously in their respective divisions and stop only when it has to signal Red,

to stop people from passing through. A robot signals Red, (i) if its previous robot is signaling Red or, (ii)

when congestion is detected in the thermal view range of this robot. That is, when each robot updates its

parameters, the densityDk (Section 3.3.2) is determined and when this density value falls in the range

23

Figure 4.6Robot are numbered starting from the main temple arena to the queue entrance. R0 is placedat the entrance of main temple arena andRn−1 is placed at the entrance of the queue.

of densities for a congestion flow (Table 4.2 - (iii)), the robot is said to havedetected a congested area.

The robot then shows Red stopping people from entering the already congested region.

4.3 Results

The results of multi-agent simulation for the temple scenario with human agents in a long queue are

presented in this section. A series of actions performed by the crowd managing agents (robots using

the method of movement described above and determined prayer timeδ to manage the crowd), are pre-

sented in the Figure 4.7.

Figure 4.7(a) shows the robots being initially introduced and placed at equal distances signaling

Green to allow people to pass through. A robotRk (here,k=1-6), moves between its adjacent robots.

Figure 4.7(b) shows that the robotR3 detects congestion in its thermal detection range and hence

signals Red until the congestion is cleared. The robotsR4, R5, andR6, signal Red as their previous

robots (R3, R4 andR5 respectively) are currently showing Red.

Once the congestion is cleared at the robotR3, it shows Green and the robotsR4,R5 andR6 showing

Red in Figure 4.7(c) are updated to signal Green as shown in Figure 4.7(d). In Figure 4.7(d), the robot

R0 shows Red as the main temple arena is not vacant.

In Figure 4.7(e), the robotR5 detects congestion and signals Red, followed by the robotR6 signaling

Red.

Table 4.4 shows states of the queue determined for certain in-flow rateλ and out-flow rateµ values

and the prayer timeδ allotted during these states.

24

Algorithm 1 Algorithm followed by Crowd managing robotic agents to detect and reduce congestion

procedure INIT ROBOT( Robot r, Pos startPos ) ⊲ All robot are initialized

r.setCurrPosition = startPos;r.setSignal(Green);r.setMoveForward();τR = curr δ; ⊲ Timestep after whichλ andµ are updated

end procedure————————procedure MOVEMENTFUNC( Robot r ) ⊲ This update is called after each simulation stepτH

r.setStartPosition = r.nextRobot().currPosition; ⊲ A robot moves in between its adjacent robots

r.setEndPosition = r.prevRobot().currPosition;r.D = r.PC/(w ∗ l); ⊲ Density in the rectangular detection range

if getRobotAt(r.nextPos()) then ⊲ Robots moves between its adjacent robots

if r.isSetForward() thenr.setBackward();

elser.setForward();

end ifend ifif r.isSetForward() then ⊲ Move in the direction of the flow towards its previous robot

r.moveStepForward();else ifr.issetBackward() then ⊲ Movie in the opposite direction of the flow towards its next robot

r.moveStepBackward();else

r.stopMove();end ifif r.prevRobot().isRed() then

r.setSignal(Red);r.stopMove();

else ifisCongested(r.D) then ⊲ Detects congestion caused due to high density

r.setSignal(Red);r.stopMove();

elser.setSignal(Green);

end ifend procedure————————procedure UPDATEFUNC( Robot r ) ⊲ This function is called each variable robot time stepτR

λ = curr λ;µ = curr µ;curr δ = getCurrPrayerT ime(λ, µ);τR = curr δ;

end procedure

25

Figure 4.7Series of actions of robots to reduce congestion.

26

In-flow rate(λ) Out-flow rate(µ) State of the Prayer time(δ)(in ped/m/min) (in ped/m/min) Queue (in seconds)

12 38 Free Flow 428 42 Free Flow 5049 58 Constant Flow 2265 32 Congestion Flow 1572 20 Stampede Flow 13

Table 4.4Prayer timeδ determined using in-flow and out-flow rates. Here,δmin=10s andδmax=50s.

Figure 4.8 The state of the queue would be determined as congestion flow, but not all the areas of thequeue are congested.

4.4 Discussion

In this method, when a robot detects congestion in its thermal view range, it shows red signal stop-

ping the people from further congesting the area. This action is followed byall the robots (next to the

robot that detected congestion) signaling Red. This stops people from passing these robots and hence

preventing the possibility of congestion. This may achieve a stampede free flow of people, but it is

not efficient. This method of movement keeps people waiting, when instead they could be allowed to

move until before they reach the congested area. Also in this method, the robots move continuously to

monitor the crowd and detect any congested areas. This is not necessary unless there are any congested

areas for the robot to detect or unless the crowd in an area that is being monitored by the robot, needs

management.

The robot that is at the main temple arena acts according to the calculated prayer time (δ). It signals

Red when the main temple arena is occupied and releases people inside the main temple arena afterδ

time and allows new set of people inside. The above results in Table 4.4, showthat people get to spend

time greater than minimum time allotted for their prayers. The prayer time and the statesof the queue

are determined using the in-flow rateλ at the entrance and the out-flow rateµ at the exit. But the queue

being very long, the states interpreted just by the calculating values ofλ andµ may not be valid. There

could be intermediate state changes in the queue. For example, in Figure 4.8, the state of the queue

determined would be constant flow or congestion flow as the people are entering the queue at a higher

27

rate than people exiting the queue. But, there is a part of the queue in between which contains a few

people moving with no forces being exerted on them (free flow of people).This part of the queue does

not need any crowd management and the people in this area could be allowedfor a longer duration to

pray. This would not happen if the prayer timeδ is determined using the flow rates at entranceλ and

exit µ. Similarly, there can be a congested area in between when the state of the queue is interpreted as

free flow. And hence, the praying time and the state of the queue determined are not appropriate.

Hence, the method of movement as well as the perspective of interpreting various states of the queue

and determining the prayer time should be modified to achieve better efficiency incrowd management.

In the next chapter, we improve these methods.

28

Chapter 5

An Extended Method of Movement for Crowd

Managing Agents

As discussed in Chapter 4, determining the state of the long queue based on the rates of people en-

tering and exiting the queue may not be valid and the method of movement of robots is not efficient.

In this chapter we present a different perspective to determine variousstates of queuing and to calcu-

late prayer time, and extend the method of movement described in Chapter 4 to improve efficiency in

management such that people get enough time to offer their prayers. The actions of robots unlike in the

method described earlier, are independent, that is a robot does not takean action considering the actions

performed by its adjacent robots.

Let each crowd managing agent determine a flow rate (λk), that is the number of people crossing

the robotRk per width (w, width of the queue) per time step (τR). If λk is the rate at which people

are entering the area between the robotsRk and robotRk−1 , and hence the flow rate of people exiting

this area would be the flow rate (λk−1) determined by the robotRk−1. That is, for the area (part of the

queue) between the robotsRk andRk−1 the rate of people entering (in-flow rate) isλk and the rate at

which the people are exiting (out-flow rate) isµk = λk−1. Thus, the long queue of human agents is

divided into small individual queues and each queue is independently managed by the robots achieving

an overall stampede free flow in the long queue. The time stepτR is equal to the prayer timeδ, so

that all the robots update their flow rate values whenever a new set of people walk into the main temple

arena. The prayer timeδ is determined based on the in-flow (λ) and out-flow (µ) rates of a queue. Since

the people flowing from the robotsR1 toR0 will next enter the main temple arena (once it is clear), the

flow rates determined at these robots are considered to calculate the prayer time. The prayer time cannot

exceed the maximum prayer time (δmax) and should be greater than the minimum prayer time (δmin).

δ(λ1, µ1, δmin, δmax) = minimum{δmin +µ1

λ1

δmin , δmax} (5.1)

Here,λ1 andµ1 (= λ0) are the in-flow and out-flow rates of the queue between the robotsR1 andR0.

29

Figure 5.1Various states of a queue between two robotsRk andRk−1

5.1 A Different Perspective of determining Various States of Queuing

Consider the part of the long queue between the current positions of robots Rk andRk−1 as an

individual queue that is managed by the robotRk. Various states of an individual queue are defined

based on the relation betweenλk andµk, the in-flow and out-flow rates of people in the queue flowing

from Rk to Rk−1 (see Table 5.1 and Figure 5.1). The range of values ofλk andµk defined for the

states of an individual queue are with respect to the range of flow rates defined for the different states of

queuing at temples (Table 4.2).

• Free Flow: Whenλk << µk, there are very few people passing through the robotRk and the

in-flow rate of people is significantly less than the out-flow rate of people.

States of an individual Queue betweenRk andRk−1

Relation between λk and µk(= λk−1) in(ped/m/min)

Free Flow 0 < λk << µk < 49

Constant Flow 49 < λk ≈ µk < 66, |λk − µk| → 0

Congestion Flow 66 < µk < λk << 82

Stampede Flow 66 < µk << λk < 82, 66 < µk << 82 < λk

Table 5.1The states of an individual queue betweenRk andRk−1 are determined using the in-flow rate(λk) and out-flow rate (µk) of people.

30

• Constant Flow: When |λk − µk| → 0, that is when people are exiting the queue at a similar

rate at which people are entering the queue, people stabilize moving with eitherconstant speed

or negligible acceleration. People entering the queue during this state push themselves into the

queue exerting force on people who are already in the queue. Any increase inλk or decrease in

µk during this state is likely to initiate congestion.

• Congestion Flow: Whenλk > µk, that is when the rate of people entering the queue is higher

than the rate of people exiting the queue, the crowd becomes agitated and people start exerting

forces which may lead to a stampede. The role of the crowd managing agents isto detect the

congestion as soon as it occurs and prevent the stampede from occurring.

• Stampede:The state of congestion flow when continues to be in the same state and ifλk >> µk,

that is people are entering the queue at a much higher rate than the rate of people exiting the

queue, this would cause stampede.

5.2 Extended Method of Movement for Robotic Agents

During the different states of queuing mentioned above, a crowd managingagent (robot) performs

different actions to reduce congestion and to prevent the occurrenceof stampedes in the queue. The

actions taken by the robotRk are based on the determined states and congestion levels. Congestion

determined by the robotRk at its current position is the density (Dk) of the crowd in the thermal sensor

detection range of this robot (see Table 2 -(iii)). When the entrance gatesare just opened at a temple,

there are few people entering with free flow in the queue, the robotRk is static showing Green signal

allowing the people to pass through. When there is constant flow,Rk moves backward (in the opposite

direction of the flow of the queue) until the queue achieves either free flowor congestion flow. During

this state of constant flow,Rk shows Red signal ifRk−1 has its signal set to Red due to congestion

ahead. This is because there is decrease in the flow rate of people atRk−1 when it is showing Red and

any significant decrease in the out-flow rate might lead the state of constantflow to a congestion flow in

the queue fromRk to Rk−1. OnceRk determines congestion flow in this part of the queue, caused due

to higher in-flow rate than out-flow rate, the robot shows Red and moves forward (in the direction of the

flow) to detect any congested regions. That is, to detect a region wherethe densityDk determined is

highest in the queue betweenRk andRk−1. The robotRk stops at this congested area (where people are

experiencing high forces), showing Red signal to stop people from further increasing the congestion.

Once the densityDk is decreased and there is increase in the out-flow rate atRk−1, Rk changes its

signal to Green.

31

Algorithm 2 Crowd Control Algorithm

procedure INIT ROBOT( Robot r ) ⊲ All robot are initialized

r.setCurrPosition = r.startPosition;r.setSignal(Green);τR = currδ; ⊲ Timestep after whichλ andµ are updated

end procedure————————procedure UPDATEFUNC( Robot r ) ⊲ This update is called after each simulation stepτH

r.setStartPosition = r.nextRobot().currPosition; ⊲ A robot moves in between its adjacent robots

r.setEndPosition = r.prevRobot().currPosition;r.D = r.PC/(w ∗ l); ⊲ Density in the rectangular detection range

if isCongested(r.D) then ⊲ Dectecs congestion caused due to high density

r.setSignal(Red);r.stopMove();

end ifif r.isSetForward() then ⊲ Move in the direction of the flow

r.moveStepForward();end ifif r.issetBackward() then ⊲ Movie in the opposite direction of the flow

r.moveStepBackward();end if

end procedure————————procedure CONTROLFUNC( Robot r ) ⊲ This function is called each variable robot time stepτR

λ = r.λ;µ = r.prevRobot().λ; ⊲ µi = λi−1

if getState(λ, µ) == “Free” then ⊲ Free Flow

r.setSignal(Green);else ifgetState(λ, µ) == “Constant” then ⊲ Constant Flow

if r.prevRobot().isRed() & getState(r.prevRobot().λ, r.prevRobot().µ) ==“Congestion” then

r.setSignal(Red); ⊲ If there is congestion in the queue ahead of the previous robot

r.setMoveBackward();else

r.setSignal(Green);r.stopMove();

end ifelse ifgetState(λ, µ) == “Congestion” then ⊲ Congestion Flow

r.setSignal(Red);r.setMoveForward(); ⊲ To detect the area that is congested

end ifcurrδ = getCurrPrayT ime(λ, µ);τR = currδ;

end procedure

32

Figure 5.2 A simulation state of queuing at temples with crowd managing agents using the extendedmethod of movement for managing the crowd.

Figure 5.3 The robotsR0, R1, R2, R3 andR4 are static and show Green. In this state people in themain temple arena are allowed forδmax time to offer their prayers.

5.3 Results

The crowd managing agents using the extended method of movement for crowd management is

briefly described using a state of the queuing simulation shown in Figure 5.2. The crowd is flowing

from left to right, that is from robotR4 located at the entrance towards robotR0 that is located at the

main temple arena. The robotsR1, R2 andR4 show Green, allowing the people to pass through these

robots. These robots are static and do not move until there is a need for detecting congestion ahead. The

robotR0 shows Red as the main temple arena is fully packed, thus stopping from more people to enter

that arena. The robotR3 shows Red stopping people from entering a congested area ahead, to prevent

any occurrence of stampede.

The simulation results after introducing the available crowd managing agents which use the method

of movement described above, at different simulation time eventst1 to t6 (t1 < t2 < t3 < t4 < t5 <

t6), are shown in Figures from 5.3 to 5.8 and Figure 5.9 shows these results on a graph of flow rates

determined by the robotsR0 to R4 vs. simulation. Figure 5.10 shows a similar graph of flow rates vs.

simulation time of about 550 simulation time steps. The prayer timeδ is calculated using the minimum

prayer time (δmin=10s), the maximum prayer time (δmax=50s), the determined in-flow rate and out-flow

rate for the queue between robotsR1 andR0.

33

Figure 5.4 This shows that the main temple arena is full and the robotR0 shows Red for aδmax

time. As there is increase in the flow rate (people entering per minute), people entering in this state areaccumulated at robotR0 until they are allowed into the main temple arena for prayers.

Figure 5.5Since people are accumulating at the robotR0, the robotR1 moves towards the main templearena to control the crowd accumulating. Once the robotR1 detects congestion in an area, it stops andshows Red stopping people from accumulating further.

Figure 5.6The main temple arena is now vacant that the robotR0 shows Green allowing people (whowere earlier accumulating atR0) to enter until the main temple arena is full. The robotR1 is Red as theflow rate at robotR0 is not high to reduce the congestion ahead ofR1.

34

Figure 5.7When the flow rate increases at the entrance, the rate of people passing the robotR4 is higherthan the rate of people passing the robotR3, and people entering the queue push themselves exertingforces on people already in the queue. In this case, the robotR4 shows Red stopping people frompassing through, there by reducing the forces experienced by peoplethat have already passedR4 untilthe flow rate atR3 is higher than the flow rate atR4 and congestion is reduced.

Figure 5.8 This shows a situation where there is free flow of people from robotsR4 to R1 andR1 ismoving towardsR0 to detect any congested areas, as there are people accumulating atR0. And R0 isshowing Red as the main temple arena is not vacant.

35

Figure 5.9The graphs of flow rate (λ) vs simulation time (t) for the robotsR0,R1,R2,R3 andR4 usingthe method of movement (Algorithm 1). The robotR0 shows Red forδ time when the main temple arenais occupied. The Red and Green dots on a graph show the changes in the signal of the correspondingrobot. The prayer timeδ for which the robotR0 shows Red, is calculated using the in-flow rateR1.λ,out-flow rateR0.µ, δmin andδmax. Hereδmin=10s andδmax=50s.

36

Figure 5.10The graphs of flow rate (λ) vs simulation time (t) for the robotsR0, R1, R2, R3 andR4

using the method of movement (Algorithm 1) for about 550 simulation time steps. This graph showsthat the robotR2 remained idle during this simulation run. Hereδmin=10s andδmax=50s.

37

5.4 Discussion

Unlike the method of movement described in Chapter 4, in this method, the robots donot move

continuously to detect any congested areas. Now that the states of individual queues between the robots

are determined using flow rates calculated by each robot, a robot moves only when the part of the queue

between itself and its previous robot seem to approach a congestion state.Figure 5.2 shows that the

robotR4 shows Green, as there is no congestion detected between itself and robotR3. That is, a robot’s

action is independent of the adjacent robots and a robot shows Red to stop people if and only if there is

congestion detected at this robot. The prayer time is determined based on the in-flow and out-flow rates

of the individual queue that is next to the main temple arena. Hence, the valueof δ is appropriate with

the state determined for this individual queue and is higher than minimum amount of time (δ) allotted

for the people to offer their prayers.

These results (Figure 5.3 to 5.8), show that the robotsR2 andR3 were always signaling Green

during the simulation (allowing people to pass through), which if removed, would not have effected the

movement of the human agents. Similarly, the graph shown in Figure 5.10 showsthat the robotR2

remained same showing Green signal through out the simulation. That is, the number of robots used is

higher than the required number of robots. Using robots more than the required number at any point of

the time during the simulation, may result in some robots being idle for major time intervals of queuing.

Situations may occur where the robots currently monitoring the queue are notsufficient to manage all

the congested parts of the queue. That is, the number of robots used would be less than the required

number of robots. Hence, we provide a method in the next chapter that uses only required number of

robots to manage the long queue.

38

Chapter 6

Required Number of Crowd Managing Robotic

Agents

The method discussed in the previous chapter uses a number of crowd managing agents (robots)

which may be is more or less than the actual number of robots required to manage the queue at a given

time. If n is the number of robots available, not all then robots would be necessary to manage the

crowd at different states of queuing. For example, when entrance of the queue is opened or when there

are very few people visiting the temple, we do not require alln robots to manage the queue, instead two

robots can be used, one at the entrance and the other at the main temple arena until congestion is likely

to occur. When congestion occurs the other robots are called as and when necessary.

6.1 Using a Required Number of Crowd Managing Agents

Sayl is the number of robots required to manage the queue at a timet, such that2 ≤ l ≤ n. The

number of robots in the queue at timet is the number of robots required (necessary) to manage the

crowd, if people do not get injured and stampedes do not occur, even when the queue is packed with

people exerting forces on each other. Thesel required number of robots manage the queue such that,

the congestion is reduced and stampedes are avoided (see Algorithm 3).

A robot is always placed at the main temple arena, which ensures that people entering the temple

arena get enough time (the calculated value of prayer timeδ) to pray. And when the queue starts in

addition to the robot placed at the main temple arena, another robot is placed at the entrance of the

long queue. Any robot that is placed at the entrance moves towards awayfrom the entrance when the

crowd starts accumulating at the previous robot. When it starts moving from the queue entrance, it

moves until it finds an area where there is a set of packed people which is likely to get congested (this is

determined using the densityDk). If a robotRk moving between the robotsRk+1 andRk−1, determines

39

Algorithm 3 Algorithm for Required Number of CMAs

procedure INIT() ⊲ When the temples gates are just opened

Robot rE = newRobot();rE.setToTempleArenaPos(); ⊲ This robot placed at the main temple arena

rE.manageMainTempleArena(); ⊲ This ensures that people inside main temple arena getδ time to offer their

prayers

Robot rS = newRobot();addRobotAtEntrance(rS); ⊲ A new robot starts from the entrance of the queue

end procedure——————–procedure ADDROBOTATENTRANCE(Robot r)

if isCrowdAccumulating(r.prevRobot()) thenr.setMoveForward();r.startControlThread(); ⊲ In addition to the steps inside the control function of Algorithm 1, checkRequired(r)

step is added.

end ifend procedure——————–procedure CHECKREQUIRED(Robot r) ⊲ This function checks if there are more or less number of robots than required in

the queue fromRk+1 toRk−1 for a robotRk

if isLessThanRequired(r) then ⊲ Checks if there are more than one congested areas with high densities

addRobotAtEntrance(newRobot());else ifisMoreThanRequired(r) then ⊲ Checks if there are no congested areas

Robot rTemp = rwhile rTemp.nextRobot() do

rTemp.setCurrPosition(rTemp.nextRobot().currPosition);rTemp = rTemp.nextRobot()

end whileremoveRobotAtEntrance();

end ifend procedure

40

Figure 6.1 Considering the queue flowing from the robotRk+1 to the robotRk−1. (i) The robotRk

determined two congested areas with very high densitiesDk(l1, l2) andDk(l1, l2). (ii) The robotRk

does not detect any high density regions.

congestion in more than one part of the queue, it then stops at the congested area that is closer to its

previous robotRk−1 This robotRk calls for initiation of a new robot iff the number of robots present

in the queue starting from the entrance of the long queue to the current location of Rk, is less than the

required number of robots to manage this queue (see Section 6.1). If a robot Rk moving between the

robotsRk+1 andRk−1, does not detect any high density regions in the queue, then the robotRl−1, that

is located closer to the entrance of the queue, is removed and the robotsRk toRl−2 (k < l− 2) take the

previous positions of their next robots, that areRk+1 toRl−1 respectively. When a robot is either added

or removed, all the robots in the queue attain a new position and are then set tocontrol mode (that is the

method movement described in Algorithm 2).

6.2 Determining the required number of robots

Consider the queue between the robotsRk+1 andRk−1. At any point of timet during the simulation,

the number of robots used in this queue, is said to be the required number of robots if the following

conditions are not satisfied (see Figure 6.1):

• (i) If there are two parts of the queue betweenl1, l2 andl3,l4, for which the densities determined

by the robotRk (Dk(l1, l2) andDk(l3, l4) respectively) are very high.

• (ii) If there are no congested areas determined the robotRk in this queue.

In case (i), the number of robots used is less than the required number of robots and in case (ii), the

number of robots used is higher than the required number of robots.

41

Figure 6.2 Two robotsR1 andR0 are initially placed at the entrance of the queue and in front of themain temple arena respectively.R0 shows Green as the main temple arena is vacant andR1 showsGreen as there is yet no accumulation atR0.

Figure 6.3RobotR0 shows Red as the main temple arena is occupied andR1 starts moving towardsR0

where people have started accumulating in front of the main temple arena, to detect any congestion.

6.3 Results

The simulation results of robots using algorithm 3 for the required number of robots and using algo-

rithm 2 for the method of movement, at different simulation time events fromt′1 to t′5 (t′1 < t′2 < t′3 <

t′4 < t′5), are shown in Figures from 6.2 to 6.6 and Figure 6.7 shows these results on a graph of flow rate

vs. simulation time for the robotsR0 toR2.

Figures 6.8, 6.9, 6.10, 6.11, show graphs of flow rate vs. simulation for theentrance and the robots

R0, R1 andR2, with varying in-flow rate at the entrance of the queue. Theδmin andδmax for this

simulation are 5s and 20s respectively.

In the Figure 6.8, from simulation timet′=0s to t′=70s, the in-flow rate at the entrance ranges from

37-50 human agents per meter per minute. During this simulation time, only two robotsR1 andR0 are

located on the track above the queue, where the robotR1 monitors the queue from entrance to the robot

R0. The robotR0 is located at the main temple arena, and allows the human agents for the determined

prayer timeδ inside the main temple arena.

42

Figure 6.4 OnceR1 detects congestion, it stops and shows Red. This is when it calls for a new robot(R2) that is placed at the entrance.

Figure 6.5 The number of people entering the queue increased suddenly at the entrance and the robotR2 detects a congestion state based on the flow rate determined. It moves towardsR1 and shows Redwhen it detects any congested area. A new robot is not called as the robot R2 detects only one regionthat is highly congested.

Figure 6.6The robotR2 is removed as the robotR1 does not detect any congested areas andR1 takesthe previous position ofR2. The robotR1 shows green as there is not yet any accumulation at the robotR0.

43

Figure 6.7 The graphs of flow rate (λ) vs simulation time (t′) for the robotsR0, R1 andR2 using themethod described in Algorithm 2 for moving and using the method described in Algorithm 3 to add orremove a robot. Here, the robotR2 is called at a later stage.

44

In the Figure 6.9, fromt′=70s to t′=90s, the in-flow rate suddenly increases upto 85 human agents

per meter per minute. Att′=81s, the robotR1 shows Red when it detects a congestion flow, which is

when another robotR2 is added at the entrance. Now,R2 monitors the queue from entrance to the robot

R1, whileR1 monitors the queue from robotR2 to robotR0.

In the Figure 6.10, fromt′=110s to t′=135s, the in-flow rate increases upto 68 human agents per me-

ter per minute and fromt′=140s to t′=220s, the in-flow rate is very low, and ranges from (0-10) human

agents per meter per minute. The robotR1, shows red att′=135s when it detects a higher density human

agents crowd and remains idle fromt′=156s to t′=214s detecting no congestion in the queue from robot

R2 to robotR0. Hence, the robotR1 is removed att′=214s.

In the Figure 6.11, fromt′=220s to t′=270s, there is no in-flow rate at the entrance and the human

agents already in the queue, experience no congestion and get to spendmaximum amount of time in

front of the deity inside the main temple arena. The prayer timeδ determined is closer toδmax. Once

the robotR1 was removed earlier, the robotR2 replacesR1, which monitors the queue from entrance to

robotR0 (or main temple arena).

Figure 6.12 combines the graphs from 6.8 to 6.11 showing a graph of flow rates determined by the

robotsR0 to R2 vs. simulation time of about 300 simulation time steps.

6.4 Discussion

The algorithm discussed in this chapter ensures that only required numberof crowd managing agents

are monitoring the queue while these crowd managing agents use the method of movement described in

Algorithm 2 (Chapter 5). The above results show that robots are being added or removed if necessary.

And the robots that remain in the queue adapt to their positions and continue to follow their methods.

This not only reduces the number of robots used at times, but only makes it easy to replace a robot when

needed, which would not be the case if all the available robots are put to use in managing the queue.

In the simulation graph shown in the Figure 6.12, the prayer time allotted for people to on an average

is δavg=11.7s. That is, people get to spend time greater than the minimum prayer timeδmin. If there

are no robots monitoring the queue, people would move until main temple arena exerting forces on each

other, which may or may not lead to a severe stampede, but, there would be congested areas with high

density crowds, that only the minimum prayer timeδmin is allotted for people to offer their prayers in

front the deity in the main temple arena. Hence, MAMAC (Multi-agent management of crowd) not only

avoids the occurrence of stampedes, but allows the people to spend substantial amount of time at their

destinations.

45

Figure 6.8 The graphs of flow rate (λ) vs simulation time (t′) for the entrance and robotsR0 andR1

from t′=0s to t′=70s.

46

Figure 6.9 The graphs of flow rate (λ) vs simulation time (t′) for the entrance and robotsR0, R1 andR2 from t′=60s to t′=130s.

47

Figure 6.10The graphs of flow rate (λ) vs simulation time (t′) for the entrance and robotsR0, R1 andR2 from t′=120s to t′=220s.

48

Figure 6.11The graphs of flow rate (λ) vs simulation time (t′) for the entrance and robotsR0 andR1

from t′=220s to t′=290s.

49

Figure 6.12The graphs of flow rate (λ) for the robotsR0, R1 andR2 vs. simulation time (t′) of about300 simulation time steps. The robotR2 is added to the track at time stept′=81s. The robotR1 isremoved at time stept′=214s there by monitoring the area from entrance of the queue to the maintemple arena.

50

TimeStamp (t)in seconds

Prayer time(δ) in sec-onds

OverallState of thequeue

24 18 Free flow53 14 Constant73 8.6 Constant85 5.7 Congestion97 6.4 Constant109 5 Congestion119 5.7 Congestion130 5.7 Congestion139 10.7 Constant152 7 Constant161 13.6 Free flow177 11.8 Constant191 15.4 Free flow211 20 Free flow234 18.6 Free flow256 15 Constant273 15.7 Constant

Table 6.1 Scenario I: Using crowd manage-ment agents to monitor the crowd.

TimeStamp (t)in seconds

Prayer time(δ) in sec-onds

OverallState of thequeue

23 20 Free flow53 20 Free flow73 10 Constant85 5 Congestion94 5 Congestion103 5 Congestion110 5 Congestion119 5 Congestion127 5 Congestion136 5 Congestion145 5 Congestion153 5 Congestion168 10 Constant181 15 Constant228 20 Free flow253 15 Free flow272 10 Constant

Table 6.2Scenario II: Using NO crowd man-agement agents.

The observations recorded in the Tables 6.1 (scenario I), 6.2 (scenario II) and the graph shown in the

figure 6.13 show the prayer time vs. the simulation time, calculated in both the scenarios (I & II).

• The average prayer time in scenario I (11.6s) is higher (by 24%) than the average prayer time in

the scenario II (9.4s).

• It also shows that in scenario II (fromt = 85 to t = 168), since there are no robots to space out

people, the situation always enters into a constantly high congested state. This situation is very

like to cause stampedes.

• Even if the congestion is not very severe to cause stampedes, a constantstate of congestion is

causing the prayer time to be the minimum possible, unlike the scenario I. That is,when crowd

managing robots are monitoring the queue, the people are stopped and movedin such a way that

the congestion does not constantly exist and thus able to increase the prayer time.

The observations shown in Tables 6.3, 6.4 are for a simulation run of very low in-flow rate which

results in a free flow state of the queue. When there is a free flow of peoplein the queue, we will be

using the minimum possible number of crowd managing agents. That is, there are only two robots mon-

itoring the queue, one at the entrance and the other at the main temple arena. And, people get to spend

maximum allotted prayer time when the queue is in a complete free flow state.

51

Figure 6.13These graphs of prayer time (δ) determined vs. simulation time (t) of about 300 simulationtime steps, compares the scenario in which no crowd managing agents are used to manage the queue,with the scenario in which crowd managing agents are used to monitor the queue.

52

TimeStamp (t)in seconds

Prayer time(δ) in sec-onds

OverallState of thequeue

27 20 Free flow62 20 Free flow102 20 Free flow137 20 Free flow169 20 Free flow202 20 Free flow241 20 Free flow278 20 Free flow

Table 6.3 Scenario I: Using crowd manage-ment agents to monitor the crowd.

TimeStamp (t)in seconds

Prayer time(δ) in sec-onds

OverallState of thequeue

27 20 Free flow62 20 Free flow102 20 Free flow137 20 Free flow169 20 Free flow202 20 Free flow241 20 Free flow278 20 Free flow

Table 6.4Scenario II: Using NO crowd man-agement agents.

TimeStamp (t)in seconds

Prayer time(δ) in sec-onds

OverallState of thequeue

18 15 Constant35 12 Constant51 8.2 Congestion62 6.3 Congestion69 5.7 Congestion78 7.4 Constant87 8.8 Constant101 8.4 Congestion112 10.2 Constant

Table 6.5 Scenario I: Using crowd manage-ment agents to monitor the crowd.

TimeStamp (t)in seconds

Prayer time(δ) in sec-onds

OverallState of thequeue

15 10 Constant28 10 Congestion39 5 Congestion47 5 Congestion56 5 Congestion64 5 Congestion75 5 Congestion83 5 Congestion92 10 Constant

Table 6.6Scenario II: Using NO crowd man-agement agents.

The observations shown in Tables 6.5, 6.6 are for a simulation run of very high in-flow rate which

may cause severe congestion. In the scenario of using crowd managing agents, the robot at the main

entrance detects the congestion and acts accordingly to control the in-flowrate. When there are no

robots, people continuously flow in to the queue, pushing themselves with highforce causing severe

congestion to lead to stampedes. The comparision of Tables 6.5, 6.6 shows that congestion (in a scenario

with robots) is brought under control and the prayer time at all simulation times determined is higher

than the minimum allotted prayer time and the average prayer time in scenario I (9.1s) is higher (by

36.4%) than the prayer time in scenario II (6.67s).

53

Chapter 7

Conclusions and Future Work

Stampedes are mass impulsive actions. Human stampedes are tragic and often occur either (i) when

people are in rush to acquire something of value, to reach a common destination, or (ii) when people are

in panic to escape from some danger, like when evacuating a building on fire. A study of stampedes oc-

curred over a period of time, showed that stampedes are frequent at religious festivals or at large crowd

gathering events (sports events and music concerts). Such stampedes are highly common in India, par-

ticularly at religious gatherings and pilgrimages, which may end in killing hundreds of people. It is a

common misconception, that the cause of deaths in these situations is trampling. Itis not simply due

to trampling, but, typically due to high forces exerted on each other leading to compressive asphyxiation.

In this dissertation, we discussed the scenario of crowding in long queuesat temples (pilgrims). At

a temple, the queue is a single directional flow of people rushing in at the queue entrance, to reach a

common destination (the main temple arena) where they can offer their prayersto a deity for some al-

lotted prayer time. Stampedes at such situations sometimes occur due to inadequate crowd management

measures. And sometimes highly congested areas are where the stampedes are initiated, but such areas

are usually not noticeable by the policemen present. Once the stampede is been initiated, controlling

the crowd that is out of order may need the involvement of forceful measures. Hence, there is a need for

crowd management and as a solution to managing crowd at such scenarios of long queues, we introduce

a set of robots which can move overhead the queue to be able to notice thosecongested areas that lead

to stampedes.

We developed a multi-agent simulation system, MAMAC (Multi-Agent MAnagementof Crowd),

to generate human agents crowd in long queues using a social force model.Crowd managing agents

(robots) are introduced into this sytem. These agents are capable of (i) monitoring the crowd at a height

above the queue, (ii) determining the crowd densities to estimate congestion levels and (iii) determining

the rates of flow of people that are used in interpreting various states of thequeue and to calculate ap-

propriate prayer time (time allotted for which people can offer their prayers). This multi-agent system,

54

moves the crowd managing agents using the algorithm developed for the methodof movement and gets

these agents to act to reduce congestion to achieve a stampede free flow. It also, adds or removes the

robots using the algorithm developed for determining the required number ofcrowd managing agents

for managing the long queue.

Method of Movement: The robots when placed on a track at a height overhead, the long queue

seems to be divided into a number of individual queues that can be monitoredand managed by each

robot to achieve an overall stampede free flow of people. The method of movement reads the current

positions of the robots and the flow rate values determined by each robot to determine the congestion

levels and states of the individual queues based on which the respectiverobots move and act to reduce

congestion.

Required Number of Robots: Not all the robots available are necessary to manage the queue at all

times. The required number of robots depend on the various states of the queue determined at different

simulation times. An algorithm was developed to add (or) remove a robot, depending on whether an

extra robot is needed to manage a congested area (or) whether a robotis monitoring an area that does

not need management, respectively.

The communication between the crowd managing agents is faster and more effective than the com-

munication between the members of a crowd management force (police or security). Our results show

that crowd managing agents can monitor the potential regions of congestion and take remedial actions

to prevent the occurrence of a stampede. Overall, the situation is under control and people get to spend

substantial amount of time, greater than the minimum allotted time infront of the deity, while using only

a required number of robots.

Future work includes developing strategies to manage the crowd in complex scenarios of queuing.

The crowd managing agents and the crowd management force can form a complimentary set of humans

and robotic agents, which can be used for managing crowds in various scenarios. And also extending

the techniques of crowd management for crowding scenarios with multi-directional flow of people.

55

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