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Simulation of Crowd Evacuation scenarios using NetLogo

Federico D'AmatoSeguir

- Simulation of crowd evacuation scenarios using NetLogo Federico D’Amato March 18, 2016 1 Introduction The aim of this work is to model the evacuation of a group of people from a simple area. The area to evacuate is represented by a simple grid; the people ﬂow from a ﬁxed number of entry-points towards a ﬁxed number of exit-points. In pedestrian simulation, most modellers focus on the locomotion level, that is, how to get from one place to another. However, pedestrian behaviour and motion does not only depend on the locomotion. It is important to include social behaviours which impact the results of the simulation. In this work we include two main social behaviours: • Altruism • Conformism With altruism we denote the propension of an individual to help a disadvan- taged person (like a disabled). In [1] this is referred as “helping behaviour”. We denote conformism as the tendency of a person to follow the most common behaviour of the others, i.e. to go in the most crowded areas of the grid. Con- formists people tend to agree with the average opinion of their neighbors while anti-conformists tend to disagree [2]. In this work we distiguish between two types of pedestrians: normals and dis- ableds. Each class of pedestrians has some characteristic attributes, such as the moving speed (obviously normal pedestrians are faster than the disabled ones). The implementation and all the simulations are performed using NetLogo 5.3 [3], which is “a multi-agent programmable modeling environment”. 1
- Figure 1: The model implemented in NetLogo. The left picture is a symmetric scenario, while the right one is asymmetric. In this example the grid is a 5 × 5 grid and each road is 4 patches large. 2 Model description In NetLogo time is discretized in ticks. In our model we also use discrete space. Every pedestrian is represented by a turtle. 2.1 NetLogo implementation & parameters In this section we brieﬂy describe how the model is implemented in NetLogo and which parameters we decide to include. The following parameters change the grid: • n-roads: this will aﬀect the size of the grid that will be (n-roads × n-roads) • roads-size: how large are the roads (in # of patches) • only-2-entries?: choose between a grid with 2 entries or with (2× n-roads) entries • only-2-exits?: choose between a grid with 2 exits or with (2× n-roads) exits • two-lines-entries?: switch between single-patches entry-points and double- patches entry-points • add-obstacles?: choose between a symmetric grid or asymmetric grid In Figure 1 there are two diﬀerent examples of grid with diﬀerent parameters. 2
- Figure 2: Sliders used to change the behavioural parameters in NetLogo Through the sliders shown in Figure 2 we can change other parameters that aﬀect the behaviour of the pedestrians in the simulation: • normal-speed: the speed for the normals pedestrians • disabled-speed: the speed for the disableds pedestrians • entry-ratio: the entry ratio for each entry-point • global-altruism: the initialization value for the parameter altruism of each normal pedestrian • global-conformism: the fraction of conformists pedestrians • conformism-radius: the ﬁxed radius (in # of patches) used in the eval- uation of the non-conformist behaviour • disabled-ratio: the fraction of disableds pedestrians Figure (2) also shows the parameters set to the default values. In our model, we deﬁne two breeds of turtles: normals and disableds. The main characteristics of these two breeds are: • normals are faster than disableds • normals are more common than disableds (we set this ratio to 20 : 1) • normals can help disableds • normals can be conformists or not, while disableds are conformists by design Every pedestrian has the following two attributes: 3
- • speed ∈ (0, 1] • altruism ∈ [0, 1] • conformist? ∈ {true, false} 2.2 Arrival process The arrival process at the i-th entry-point is geometrically distributed, i.e. we generate a pedestrian at entry-point i at the k-th tick if the entry-point is free and x(k) ∈ X ∼ U[0, 1] < λi (1) where U[0, 1] is the uniform distribution and λi is the entry-ratio of entry i. 2.3 Moving behaviour In our model, in one tick one pedestrian can move only by one position, chosen with some criterion in his neighborhood (we consider cross-like neighborhoods). At each tick, every pedestrian decides whether to move or not according to his speed. Each pedestrian’s speed express the probability to move in one tick. The moving behaviour is explained in Algorithm 1. Algorithm 1: Moving behaviour, i-th pedestrian, k-th tick 1 if # free patch in my neighborhood > 0 then 2 choose y(k, i) ∈ X ∼ U[0, 1] 3 if y(k, i) < speedk i then 4 Move to a free patch in the neighborhood according to some criterion 2.4 Altruism At each tick, every normal turtle decides whether to help or not a disabled in his neighborhood. The helping behaviour is explained in Algorithm 2. Instruction 7 of Algorithm 2 has 2 meanings: on one hand, it means that each normal pedestrian can help at most one disabled; on the other hand it means also that if a pedestrian choose not to help a disabled at time k, he will not help anybody else in the future. We will use the term altruists for those pedestrian who execute Instruction 5 at least one time, while we will call non-altruists the others. 2.5 Conformism The moving strategy used in Instruction 4 of Algorithm 1 strongly depends on the attribute conformist? of the pedestrian. 4
- Algorithm 2: Helping behaviour, i-th pedestrian, k-th tick 1 if altruismk i > 0 then 2 if # disableds in my neighborhood > 0 then 3 choose a(k, i) ∈ X ∼ U[0, 1] 4 if a(k, i) < altruismk i then 5 Help a random disabled j in my neighborhood 6 speedk+1 i = speedk i +speedk j 2 7 altruismk+1 i = 0 2.5.1 Conformist behaviour Conformists pedestrians aim to the nearest exit-point regardless of how crowded the path is. The conformist behaviour is explained in Algorithm 3. Algorithm 3: Conformist behaviour, i-th pedestrian, k-th tick 1 Let nearest-exitk i the nearest exit 2 Compute headingk i as the angle between me and nearest-exitk i 3 for each free patchj in my neighborhood do 4 Compute heading-patchj as the angle between patchj and nearest-exitk i 5 Let best-patchk i = arg minj |headingk i − heading-patchj| 6 Move to best-patchk i 2.5.2 Non-Conformist behaviour Non-conformists pedestrians have a more complex behaviour. They try to avoid overly crowded paths; if the path to the nearest exit is too crowded, a non- conformist pedestrian change his mind and heads to another exit. The non- conformist behaviour is explained in Algorithm 4. Instruction 5 of Algorithm 4 deserves some explanations. We have two condi- tions: • nnearest > α express the fact that the path between the pedestrian and the nearest exit-point is too crowded. α is a parameter of the model. • nsecond < nnearest express the fact that the second exit-point in less crowded than the nearest exit-point. If these two conditions are satisﬁed, the non-conformist pedestrian heads to the second nearest exit-point instead of the nearest one. 5
- Algorithm 4: Non-Conformist behaviour, i-th pedestrian, k-th tick 1 Let nearest-exitk i the nearest exit 2 Let alternative-exitk i the second nearest exit 3 Compute nnearest as the number of pedestrian between me and nearest-exitk i in a ﬁxed radius 4 Compute nalternative as the number of pedestrian between me and alternative-exitk i in a ﬁxed radius 5 if (nnearest > α) and (nalternative < nnearest) then 6 Compute headingk i as the angle between me and alternative-exitk i 7 preferred-exitk i = alternative-exitk i 8 else 9 Compute headingk i as the angle between me and nearest-exitk i 10 preferred-exitk i = nearest-exitk i 11 for each free patchj in my neighborhood do 12 Compute heading-patchj as the angle between patchj and preferred-exitk i 13 Let best-patchk i = arg minj |headingk i − heading-patchj| 14 Move to best-patchk i 6
- 0 100 200 300 400 500 600 700 800 900 1,000 0 0.2 0.4 0.6 k Fi,j(k) Entry 1 Exit 1 Exit 2 0 100 200 300 400 500 600 700 800 900 1,000 0 0.5 1 k Fi,j(k) Entry 2 Exit 2 Figure 3: Cumulative distribution function of sojourn time for diﬀerent pairs Entry-Exit 3 Experiments 3.1 Default settings In all the following experiments we use the default parameters values as shown in Figure 2. The model studied is the right one of Figure 1, that is an asymmetric model with two entry-point and two exit-points, 5 roads each of which is 4 patches large. In our experiments we compare the results obtained from a single simulation with the results obtained as the average over 10 diﬀerent simulations. 7
- 3.2 Numerical results Let i an entry-point and j an exit-point, we can deﬁne the cumulative distribu- tion function of the sojourn time of pedestrians as: Fi,j(k) = P {exit at Exitj with sojourn time ≤ k | enter at Entryi} (2) Figure 3 shows Fi,j(k) for all the Entry-Exit combinations. As we can see from Figure 3, using the default settings, pedestrians that enter from Entry 2 always exit in Exit 2. On the other hand, pedestrians that enter from Entry 1 exit both from Exit 1 or Exit 2. In particular, with the default settings, we have: P1,1 = P {exit at Exit1| enter at Entry1} = 0.574 P1,2 = P {exit at Exit2| enter at Entry1} = 0.426 P2,1 = P {exit at Exit1| enter at Entry2} = 0.000 P2,2 = P {exit at Exit2| enter at Entry2} = 1.000 (3) From now on, we try to characterize how Pi,j changes with diﬀerent values for the model’s parameters. The ﬁrst parameter under exam is entry-ratio. As we can see in Figure 4, this parameters strongly aﬀects the value of P1,1: for near-zero values of entry-ratio, P1,1 is high, i.e. pedestrians that enter from Entry 1 have an high probability to exit from Exit 1. As the entry-ratio increases, P1,1 de- creases; this represents the fact that when our model becomes too crowded, non-conformists pedestrians head to the secondary exit more and more often. The second parameter that aﬀects the value of P1,1 is conformism. In Figure 5 we plot P1,1 as a function of conformism, using three diﬀerent roads-size in the model. As we can see in Figure 5, in a model with roads-size = 2, conformism doesn’t aﬀect the value of P1,1. With larger values of roads-size, however, we can notice some sort of linear dependency between P1,1 and conformism. This is caused by the fact that, increasing the number of conformists pedestrians, we increase the number of pedestrians that choose the nearest exit (i.e Exit 1) regardless of how crowded the path is. Another important measure of our simulations is the average sojourn time of the pedestrians, that is the time taken from the pedestrians to pass through our model. Figure 6 shows how the average sojourn time changes with the entry-ratio. The ﬁrst consideration to be done is that the average sojourn time is larger for the pedestrians that enter from Entry 2. Using low values of entry-ratio, the sojourn time is relatively small. As the entry-ratio increases, the sojourn time increases; however, when the entry-ratio becomes larger than 0.2, it becomes practically constant. The most obvious parameter to take into account when we study the average sojourn time is the speed of the pedestrians. Since the movement of pedestri- ans is geometrically distributed with rate speed, the expected value of sojourn time for the i-th pedestrian (not considering the other factors such as traﬃc or altruism/conformism) is: E[S] = d speed (4) 8
- 0 0.2 0.4 0.6 0.8 1 0.55 0.6 0.65 0.7 0.75 0.8 0.85 Entry ratio P1,1 Entry 1 Exit 1 Exit 1 (10 attempts) Figure 4: Fraction of turtles that enter from Entry1 and exit in Exit1 for dif- ferent values of the entry-ratio 9
- 0 0.2 0.4 0.6 0.8 1 0.4 0.45 0.5 0.55 0.6 0.65 0.7 Conformism P1,1 Entry 1 Exit 1 (roads-size=2) Exit 1 (roads-size=2, 10 attempts) Exit 1 (roads-size=4) Exit 1 (roads-size=4, 10 attempts) Exit 1 (roads-size=6) Exit 1 (roads-size=6, 10 attempts) Figure 5: Fraction of turtles that enter from Entry1 and exit in Exit1 for dif- ferent values of the conformism and roads-size 10
- 0 0.2 0.4 0.6 0.8 1 200 220 240 260 280 300 320 340 360 380 Entry ratio Averagesojourntime(#ticks) Entry 1 Entry 1 (10 attempts) Entry 2 Entry 2 (10 attempts) Figure 6: Average sojourn time (in # of ticks) of pedestrians that enter from Entry1 and Entry2 for diﬀerent values of the entry-ratio 11
- where d is the (ﬁxed) distance between Entry 1 and Exit 1 (or Entry 2 and Exit 2) and speed is the average speed of the pedestrians. Figure 7 shows that using a low value of the entry-ratio, the average sojourn time of pedestrians is nearly E[S]. When we set the entry-ratio to an higher value, the average sojourn time increases: this happens because of the traﬃc in the area caused by the high entry-ratio. 12
- 0.2 0.4 0.6 0.8 1 100 200 300 400 Normal Speed Averagesojourntime(#ticks) Entry 1 (entry-ratio = 0.001) Entry 2 (entry-ratio = 0.001) E[S] 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1,000 1,200 1,400 1,600 Normal Speed Averagesojourntime(#ticks) Entry 1 (entry-ratio = 1.00) Entry 2 (entry-ratio = 1.00) E[S] Figure 7: Average sojourn time (in # of ticks) of pedestrians that enter from Entry1 and Entry2 for diﬀerent values of normals speed and entry-ratio 13
- 4 Conclusions In this work is presented a Netlogo implementation of a variety of crowd evac- uation scenarios. The model is highly customizable, in terms of the structure the area to evacuate and in terms of the pedestrians’ behaviours. In particular, we have implemented two social behaviour: altruism and conformism. Thanks to the ﬂexibility of the model, we were able to study how this two behaviours can aﬀect the values of: • the cumulative distribution function of the sojourn time for all the en- try/exit pair • the probability of the pedestrian to exit using an exit-point instead of another one • the average sojourn time of the pedestrians in the area Even if this work presents a reasonable set of experiments, more tests can be done using diﬀerent default settings. In particular it might be interesting to use diﬀerent types of asymmetries in the grid. References [1] I. von Siversa, A. Templetonc, G. K¨ostera, J. Druryc, A. Philippidesc, Hu- mans do not always act selﬁshly: social identity and helping in emergency evacuation simulation, 2014. [2] F. Bagnoli, R. Rechtman, Bifurcations in models of a society of reasonable contrarians and conformists, 2015. [3] Netlogo, http://ccl.northwestern.edu/netlogo/, 1999. 14