regime I:

regime II:

regime III:

Mirko Kämpf and Jan W. Kantelhardt

Abstract Our evacuation simulation tool utilizes established algorithms for the emotional and intelligence driven motion of human beings in addition to a simple lattice gas simulation. We analyse the spread of information inside a restricted geometry of a real building and compare these results with the data from a simulation in the free space. We apply the DFA and the RIS statistic to our simulation dataset to detect phases or phase transitions of the whole system. We study the impact of communication technology by comparison of different update algorithms and exit strategies. These results help us to define basic functional requirements to the underlying communication technology and network topology as well as to the needed sensors.

Information Spread in the Context of Evacuation OptimizationInstitut für Physik, Fachgruppe Theoretische Physik,

Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany

Acknowledgement

We thank the EU for funding.

Motivation There are many approaches for an optimization of the process of evacuation of large buildings or areas. One of them is to use signals, sometimes dynamical controlled from outside, for routing the people to the next exit or cars to the next free lane on a street. A much better strategy could be, to use information about the neighborhood of a person or a car. Lots of sensors and „intelligent“ devices are already available. They can measure properties of the real world. Other devices can transmit this data to other persons.

But what rules for the routing of persons and that rules for the best decision of a person are the best in the context of the whole system?

How can we describe the system, with physical properties and how can we find transitions in the state of such a system? To support the development of such a toolset in the SOCIONICAL project we do numerical simulations.

Analysis of the Influence of AmI Technologie on the Agents Motion and on Information Flow [2,3]

Rules for Routing and Quality of Information

Information Spread in Open vs. Restricted Geometry [1]

Model & Simulation Techniques

DY 10.30

References[1] K. Kloch et al.; Ad-hoc Information Spread Between Mobile Devices ...; Proceedings of ARCS 2010, Vol. 5974 of Lecture Notes in Computer Science, 101–112. Springer, 2010.

[2] R. Holzer et al.; Quantitative Modeling of Self-Organizing Properties; In Proc. of 4th Int’l. Workshop on Self-Organizing Systems, Zurich, Dec. 9-11 2009, Springer, LNCS.

[3] C. Auer et al.; A Method to Derive Local Interaction Strategies for Improving Cooperation in Self-Organizing Systems; In Proc. of 3rd IWSOS, Vienna, Dec. 10-12 2008. Springer, LNCS.

[4] P. Gawronsky et al.; Evacuation in the Social Force Model is not stationary; (submitted, arXiv:1103.0403).

[5] D. Chowdhury et al.; Statistical Physics of Vehicular Traffic and some Related Systems; Physics Reports, 329 (2000) 199-329.

Outlook• Can we detect phase transitions of the whole system by looking only at the fluctuation properties of several values?

• Are there any agents with some kind of synchronization, with or without direct radio links between them?

• Does the communication flow affect the total evacuation time and how is this dependency defined?

• Can we define communication rules for an optimization of the total evacuation process?

Contact mirko.kaempf@physik.uni-halle.de

Statistical Time Series Analysis (DFA, RIS) [4,5]

But how can an agent determine how reliable such an information really is?

Every time an existing map is merged with a received one, a special weight has to be given before the calculation of the average data.

Depending on the time since a fact was recognized the information is less relevant. So we can define a current information map in every time step.

d

During the evacuation of the the agent its speed and its average speed in a single sector of its way are determined. This information is put into a map for each way the agent passed. In the cross sections a routing decision tells the agent which way to go. If there is some information about the properties of the way, the decision is easier.

In this way an agent can find an optimized way if he has a map with the current properties of the flow through the building.

The numbers on the edges show the time an agent will need to pass this way. Based on this information, if it was received, the agent is able to determine the best direction to go.

The sketch shows a part of a building with moving agents. Every agent has information about the fields he was before. By using radio technology it can share this information with other agents. If the radio range is larger then distance between the floors d, the agents in the upper floors can use this information for routing.

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corridor with x boxes stairway with y boxes

prefered exit

Agents have a simple structure and represent(i) individual persons or(ii) persons with AmI device,(iii) groups of persons.

They behave similar as molecules of gas, with few additional rules

They are reflected by other agents or walls and have to wait if there is a jammed path

We aim at studying phase transitions

AmI based information spread

Lattice gas model with

1. ‘stupid’ agents (like gas)2. different roles (speed / types like staff, rescue worker, normal people)

Input: simulation geometry (symmetry) (AGH)

Simplified analytical

(mean field) theory

compare

Simulation of lattice gas model with agents

representing (i) person(ii) person & AmI device

(iii) group of people

integrate

Emotion spread & group formation

Input: Strategies and parameters for

information spread (U Passau)

Input: Parameters from agent models

(VU Amsterdam)

#of floors #of floors

0 2000 4000 6000 #of agents

0 2000 4000 6000 #of agents

t40

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60

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80

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1000

0

t MW

20

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3000

4000

5000

Results of the numerical simulations total evacuation time mean evacuation time

Scaling Theory: Generalizing the Numerical ResultsWe find three regimes for the evacuation behavior:

(1 )Low density – not all floors are occupied

(2 )Medium density – smooth evacuation

(3 )High density – jammed staircases

The curves from different simu-lations can be scaled on top of each other if the quantities are

divided by the system size #of agents / # of floors

(2( )3)

Include emotion / information spread in scaling theory Ratio of infected agents Infection rates determined

in different regimes

Results from Detrended Fluctuation Analysis

Results from Return Interval Statistics

In a cooperation with the University of Passau some quantitative statistical measures are applied to the system for optimization of the local strategies. We want to analyze the best communication strategy and the best routing strategy for the agents. What is better, to rely only on local data with an assumed good quality or is it more efficient to spread the data through the whole system? What data do the agents need in what situation? How many agents do need the information?

Measure of Target Orientation For a calculation of the measure of target orientation of a system we have to define a value, which represents the optimized target of the process. In our scenario, the target is reached if all agents are evacuated. The simulation results are calculated based on different rules and parameter sets. By an analysis of the target orientation depending on the rules and parameters the best rules an the optimized parameter sets can be detected.

Resilience with respect to an external eventThe measure of resilience shows, how ressistent a system is in respect to undetermined external events like the breakdown of the stair case or a blocked exit in our evacuation scenario. Like in the case of the measure of target orientation special rules and parameter sets are analyzed: What rule and what parameter set are most efficient in the context of what kind of external event?

Measure of Emergence of communication patternsDuring the exchange of information between agents, specific patterns can emerge. Such dependencies or communication patterns can be detected and analyzed by calculating the value of emergence.

a) b)

But because of the memory of the system and its dynamical properties an agent will never have fully correct data.

In contrast, a theoretical external instance has always the correct data for every point in the map. So we can calculate the difference between the real value and the value an agent assumes by using its map. This gives us a criterion for the optimization of the information exchange algorithms and radio properties in our simulation.

Fig a) shows the „Fundamental Diagramm“ for measured speed and density values on a highway. Each Point shows a 15 min average. Based on known rules for phase definitions the points are colored green for free flow, blue for synchronized flow and red for traffic jam. For each part all time series with a constant phase, the fluctuation function (fig b) was calculated. If the slope of F(s) is about 0.5 the data is uncorrelated. If the slope is higher, like in the red curve, there is a correlation in the data.

Although we do not have as many data points as in a traffic scenario, we want to study such a „Fundamental Diagramm“ for pedestrians movement during the evacuation process.

The aim is, to identify typical properties to describe the systems state based in the measurement on individuals or special points.

One aim is, to use an analytical model to predict global properties of large-scale information technology systems from the parameters of simple local interactions. The first example is intended as a step towards using complex systems modeling methods to control self-organization in organic systems. It is motivated by a concrete application scenario of information distribution in emergency situations, but is relevant to other domains such as malware spread or social interactions. Specifically, it was shown how the spread of information through ad-hoc interactions between mobile devices depends on simple local interaction rules and parameters such as user mobility and physical interaction range (radio range R). As a first result three qualitatively different regimes of information `infection rate‚ K can be analytically derived and validate the model in extensive simulations. One special property of this model is the unrestricted geometry in which the agents can move. In our model, the geometry is defined by the building. How does this affect the flow of information or the infection rate? Can we find comparable analytical descriptions of the information flow depending on the local rules and strategies?

Infection ratio K plotted versus radio range R for N = 512, L = 2000 and 2 ≤ R ≤ 75 in part (a). Vertical lines c1 and c2 mark the separations of the three regimes.Scaled simulation results for various N compared with the analytical value of K computed according for the first regime is shown in part (b).

First results for simulations in a restricted geometry show comparable result to the previous simulations in a free space.

The infection rate depends obviously on the radio range. This simulations have to be repeated with other rules for the movement of the agents and with other geometrical properties.

So we can study what parameters and what strategies influences the information spread in which way.

R1 R2

We plan to apply two statistical methods which were used in previous work with comparable datasets to the simulation results.

F(s)

We analyzed the time lag between the exit of two following persons during an evacuation simulation based on the social force model. The Distributions P(r) (fig. a) and the scaled distributions R · P(r/R) (fig b) of the time lags r with mean R a given number of persons remaining in the evacuated room are plotted. The unscaled distributions in (a) show that the nearly Gaussian peak for short time lags is hardly changing, while the exponential tail is decaying with decreasing n. The scaled distributions in (b) show that the mean R characterizes the exponential peak fairly well.

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