Measuring Self-organisation at Runtime

A Quantiﬁcation Method based on Divergence Measures

Sven Tomforde

, Jan Kantert

and Bernhard Sick

Intelligent Embedded Systems, University of Kassel, Wilhelmsh

oher Allee 73, 34121 Kassel, Germany

Institute of Systems Engineering, Leibniz Universi

at Hannover, Appelstr. 4, 30169 Hannover, Germany

Keywords:

Self-organisation, Quantiﬁcation of Self-organisation, Organic Computing, Adaptivity, Probabilistic Models,

Communication Patterns.

Abstract:

The term “self-organisation” typically refers to the ability of large-scale systems consisting of numerous au-

tonomous agents to establish and maintain their structure as a result of local interaction processes. The moti-

vation to develop systems based on the principle of self-organisation is to counter complexity and to improve

desired characteristics, such as robustness and context-adaptivity. In order to come up with a fair comparison

between different possible solutions, a prerequisite is that the degree of self-organisation is quantiﬁable. Even

though there are some attempts in literature that try to approach such a measure, there is none that is real-world

applicable, covers the entire runtime process of a system, and considers agents as blackboxes (i.e. does not

require internals about status or strategies). With this paper, we introduce a concept for such a metric that

is based on external observations, neglects the internal behaviour and strategies of autonomous entities, and

provides a continuous measure that allows for an easy comparibility.

1 INTRODUCTION

In 1991, Marc Weiser formulated his vision of “ubiq-

uitous computing” (Weiser, 1991) which predicted

that individual devices such as personal computers

will be replaced by “intelligent things” and these

things support humans in an imperceptible manner.

A fundamental prerequisite for such a pervasive sys-

tem serving humans in their daily lives is the abil-

ity of distributed technical devices to self-organise.

Since a centralised or even human controlled process

is not applicable due to the sheer amount of deci-

sions to be taken, the interdependencies among dis-

tributed elements, and the resulting complexity. As

a consequence, initiatives such as Proactive (Tennen-

house, 2000), Autonomic (Kephart and Chess, 2003),

and Organic Computing (Tomforde et al., 2011) or

Complex Adaptive Systems (Kernbach et al., 2011)

emerged that investigate large-scale self-adaptation

and self-organisation processes.

Although there is no commonly agreed deﬁni-

tion of the term, the basic concept related to self-

organisation typically means that the structure of the

overall system is dynamic (i.e., time-variant), and

the adaptations causing these dynamic changes are

done by the entities forming the system. More pre-

cisely, the system consists of autonomous entities and

these entities decide with which other entity they in-

teract (e.g., to solve a task or to exchange informa-

tion). In the context of this paper, we will consider

the structure of a system being identical with the rela-

tions among distributed entities (i.e., subsystems or

agents in the terminology of multi-agent systems).

We further assume that such a relation has a func-

tional meaning, i.e., it deﬁnes an interaction that sup-

ports the functionality of the overall system.

The underlying hypothesis of all the aforemen-

tioned initiatives is that self-organisation is beneﬁ-

cial in comparison to traditional, centralised solu-

tions; and that this beneﬁt can be expressed in terms

of aspects such as higher robustness, higher efﬁ-

ciency, or reduced task complexity, for instance—see

e.g. (M

uller-Schloer et al., 2011; Wooldridge, 2009).

However, some work suggests that neither the fully

self-organised nor the fully centralised organisation

blueprint will result in the most efﬁcient (or even opti-

mal) behaviour. One particular example from our own

preliminary work can be found in establishing pro-

gressive signal systems for urban road trafﬁc control,

see (Tomforde et al., 2008). Here, nodes (i.e., inter-

section controllers) coordinate themselves to improve

the overall trafﬁc ﬂow. As a consequence, the system

Tomforde S., Kantert J. and Sick B.

Measuring Self-organisation at Runtime - A Quantiﬁcation Method based on Divergence Measures.

DOI: 10.5220/0006240400960106

In Proceedings of the 9th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2017), pages 96-106

ISBN: 978-989-758-219-6

structure in terms of coordination schemes emerges as

a result of local interactions—self-organisation takes

place. However, a fully self-organised solution is not

beneﬁcial in some cases—while, in turn, a fully cen-

tralised solution is not fast enough. As a consequence,

hybrid approaches have been developed that apply

self-organisation to a certain degree (Tomforde et al.,

2010a).

A meaningful comparison between different solu-

tions to the same problem area is twofold—if done

correctly: it founds on desired metrics (e.g., robust-

ness, utility) and accompanied cost (e.g., communi-

cation and computation overhead). However, to or-

der these attempts according to the system organisa-

tion, a third metric has to be applied: a quantiﬁca-

tion of the degree of self-organisation. To estimate

the degree of self-organisation, the runtime behaviour

of a system has to be evaluated—without the need

of accessing internal logic and status of autonomous

entities: In increasingly open and interwoven sys-

tem structures consisting of autonomous agents (Tom-

forde et al., 2014; H

ahner et al., 2015), we have to

deal with systems that we do not control and that we

have not developed—we can just observe their be-

haviour from the outside. In this paper, we develop

a concept for such a metric that is real-world applica-

ble, covers the entire runtime process of a system, and

considers agents as blackboxes (i.e., does not require

internals about status or strategies), see (Wooldridge,

2009). It can be used to quantify how much self-

organisation is observed—in contrast to classifying

systems as being either purely self-organised or cen-

tralised. We can further use the metric to distinguish

between such cases.

The remainder of this paper is organised as fol-

lows: Section 2 brieﬂy summarises the state-of-the-

art. Afterwards, Section 3 describes the underlying

system model, the assumptions and preliminary work.

Section 4 introduces the novel approach to quantify

self-organisation in technical systems. Section 5 anal-

ysis the behaviour of the measurement in terms of an

exemplary scenario. Finally, the paper closes with a

summary and an outlook in Section 6.

2 STATE OF THE ART

The term “self-organisation” is increasingly used in

literature, covering a variety of domains such as math-

ematics (Lendaris, 1964), thermodynamics (Nicolis

and Prigogine, 1977), or information theory (Shal-

izi, 2001). In addition, non-technical considerations

have been discussed, see e.g. (Heylighen, 1999) for

an overview. Thereby, the term is typically used to de-

scribe effects where a certain structure emerges with

a bottom-up perspective—meaning as a result of au-

tonomous processes.

In systems engineering, especially in the con-

text of initiatives such as Organic (OC) and Auto-

nomic Computing (AC), methods to transfer classic

designers’ and administrators’ decisions to the re-

sponsibility of the systems themselves are investi-

gated. As a result, the relevance of a phenomenon

of self-organisation is ubiquitously accepted—but a

commonly agreed notion or deﬁnition of its charac-

teristics is not existing. Instead, a variety of some-

times contradictory deﬁnitions and descriptions are

observed.

Many natural and social systems served as inspi-

ration to frame the understanding of the term self-

organisation—ranging from work organisation in ant

colonies, see (Dorigo and Birattari, 2010) for a techni-

cal imitation, to ﬂow formations in pedestrian move-

ments, see (Helbing, 2012). By external observation,

humans recognise an increase of order (e.g., in terms

of pattern forming)—a behaviour is produced that in

some way can be called “organised” (i.e., generating

some kind of structure). In addition, Polani refers to

this observation as self-organisation if the “source of

organisation is not explicitly identiﬁed outside of the

system” (Polani, 2013).

Continuing the previous discussion, Polani deﬁnes

self-organisation as a “phenomenon under which a

dynamical system exhibits the tendency to create or-

ganisation out of itself, without being driven by an

external system” (Polani, 2013). Unfortunately, this

deﬁnition—the same holds for others—is pretty close

to that of emergence. As a result, many attempts can

be found where emergence and self-organisation are

compared and distinguished from each other, e.g., in

(Shalizi, 2001). However, if no clear notion of both

terms is given, a separation is hardly possible.

In the context of OC, M

uhl et al. proposed a for-

mal classiﬁcation of technical systems with the pur-

pose to deﬁne a class for “self-organising technical

systems” (Muehl et al., 2007). Their classiﬁcation

is founded on Zadeh’s notion of “adaptivity” (Zadeh,

1963) and introduces a hierarchical structure: from

self-manageable at the bottom layer to self-managing

and to self-organising. They consider a system as

self-organising “if it is (i) self-managing, i.e., the sys-

tem adapts to its environment without outside con-

trol, (ii) structure-adaptive, i.e., the system establishes

and maintains a certain kind of structure (e.g., spatial,

temporal) regarding the system’s primary functional-

ity, and (iii) employs decentralised control, i.e., the

system has no central point of failure” (Muehl et al.,

2007). From the perspective of this paper, insisting on

Measuring Self-organisation at Runtime - A Quantiﬁcation Method based on Divergence Measures

a complete absence of external control is not desirable

since user inﬂuence is part of the overall concept, see

(Tomforde et al., 2011) as one example. However, the

classiﬁcation gives a valuable guideline to what we

need as basis for deﬁning self-organisation in techni-

cal systems.

Besides these conceptual approaches to self-

organisation, more formal methods have been pro-

posed that try to come up with a quantiﬁcation of self-

organisation in technical systems. As a result of the

heterogeneous origins for working on self-organised

systems, a variety of attempts to measure and quan-

tify it have been made. A ﬁrst example has been in-

troduced by Shalizi et al. (Shalizi and Shalizi, 2003;

Shalizi et al., 2004). They presented a mathematical

model following Shannon’s entropy and deﬁned self-

organisation as a process that is characterised by an

increase in the amount of information needed to fore-

cast the upcoming system behaviour. The basic idea is

that the increase of internal complexity, i.e., without

external intervention, relates to the increase of self-

organisation. The method works on the basis of ob-

servable attributes, such as location (i.e., coordinates)

or sensor readings (e.g., temperature or speed).

Similarly, Heylighen et al. (Heylighen, 1999;

Heylighen and Joslyn, 2001) presented a concept to

use the statistical entropy as basis to determine a so-

called “degree of self-organisation”. Here, a system

that is stuck in an attractor within the state space is

deﬁned to be self-organised, since the system cannot

reach other states any more. Consequently, a decrease

in statistical entropy can be observed which results in

an increase of order—that in turn is used as measure-

ment for self-organisation. The main message here

is that self-organisation results in stable solutions—

external inputs such as disturbances are needed to

restart the organisation process again.

Closely related is the concept proposed by

Parunack and Brueckner in the context of Multi-

Agent Systems (Van Dyke Parunak and Brueckner,

2001). They use an entropy model in combination

with the Kugler-Turvey model with the purpose to

combine systems with decreasing and increasing or-

der. In their work, a macro- and a micro-level in-

stance of a system are coupled and the information

entropy is used to determine the particular degree of

self-organisation for each abstraction level. The main

insight from this example is that self-organisation af-

fects different abstraction layers.

Furthermore, Wright et al. (Wright et al., 2000;

Wright et al., 2001) focussed on an attractor-oriented

concept for considering self-organisation. They dis-

cussed an approach to measure self-organisation by

using entropy as a function of an attractor’s dimen-

sionality within the underlying state space. Here, a

self-organised system requires an attractor—while the

organisation is considered according to Polani’s no-

tion (Polani, 2003). Following this approach, the au-

thors deﬁne a system to be self-organised if the dy-

namics of organisation information grow during op-

eration and in correspondence with these dynamics.

As one conclusion of the work, we can state that self-

organisation has a process perspective and is not just

a static characteristic of the system.

Gershenson et al. considered self-organisation as a

process opposed to emergence (Gershenson and Fer-

nandez, 2012). Therefore, they measured emergence

using Shannon’s entropy formula again, and deter-

mined self-organisation as decrease of emergence

over time. In general, Gershenson claims that in artiﬁ-

cial self-organising systems (i.e., engineered systems)

“structure and function should emerge from interac-

tions between the elements” (Gershenson and Fernan-

dez, 2012). This implies that the system’s purpose is

neither designed or programmed, nor controlled. In

contrast, components should interact freely and mutu-

ally adapt towards a stable solution—also referred to

as ﬁnding a “preferable” setting through emergence

(Gershenson and Heylighen, 2003). In the context

of this paper, we focus on purpose-oriented systems

engineering—hence, letting the system ﬁnd “some-

thing” is not an option.

OC came up with its own approach to—what they

called—“controlled self-organisation”, see (Schmeck

et al., 2010). They deﬁne a corridor for being self-

organised by using the maximum (no external inter-

vention for building structural patterns) and minimum

(extrinsically organised) boundaries. Following this

concept, a quantiﬁcation of self-organisation is done

by considering the control mechanisms being respon-

sible for structure adaptations. For an adaptive system

S consisting of 1) m elements (with m > 1) that have

a large degree of autonomy and 2) k control mecha-

nisms (k ≥ 1), the degree of self-organisation can be

indicated as (k : m).

Summarising the previous discussion of the term

“self-organisation” in literature, we can initially state

that there are highly heterogeneous notions and un-

derstandings of what the term comprises. Most of

the discussed statements provide only a very basic ap-

proach to understanding when systems can be called

self-organised. Also, there is typically either a non-

technical perspective applied or the concept lacks a

consideration of organisation in the sense of a techni-

cal system structure.

ICAART 2017 - 9th International Conference on Agents and Artiﬁcial Intelligence

3 ASSUMPTIONS AND SYSTEM

MODEL

In the following, we deﬁne self-organisation as a con-

tinuous process to establish, change, and maintain a

system structure in terms of relationships between au-

tonomous subsystems (or agents). This process is per-

formed by the participating autonomous agents them-

selves, and it is utility-driven. This means that varying

external (and/or internal) conditions require different

system structures (and maybe even compositions in

terms of participating subsystems), which can be ex-

pressed in relation to a certain system goal. This sys-

tem goal, in turn, can be expressed by a given utility

function U. If the subsystems act without external

inﬂuences, i.e., their behaviour is controlled only by

adapting U, we call these subsystems autonomous—

which corresponds to the term agent where a com-

puter system acts on behalf of a user (Wooldridge,

2009).

3.1 System Model

From a conceptual point of view, we assume a self-

organising system S consisting of a potentially large

set of autonomous subsystems a

∈ A. Each a

equipped with sensors and actuators. Internally, each

distinguishes between a productive part (PS, re-

sponsible for the basic purpose of the system) and a

control mechanism (CM, responsible for controlling

the behaviour of PS and deciding about relations to

other subsystems). This corresponds to the separation

of concerns between System under Observation and

Control (SuOC) and Observer/Controller tandem in

the terminology of OC, see (Tomforde et al., 2011).

Figure 1 illustrates the basic system with its input

and output relations. However, this is just used to

highlight what we mean by referring to autonomous

subsystems. In particular, the user guides the be-

haviour of a

using U and does not intervene at de-

cision level—actual decisions are taken by CM.

Productive System

Control Mechanism (CM)

Sensors Actuators

ENVIRONMENT

Observation

of raw data

Execution of

interventions

Goals

User

Figure 1: Schematic illustration of an autonomous subsys-

tem.

We do not restrict the system composition, i.e., we

allow open systems. However, to deﬁne the system

boundaries within analysis, we require to deal with a

set of agents that potentially participate in the overall

system during a certain period of time. Furthermore,

we do not require to have full access to each agent

: Each agent can belong to different authorities, can

be controlled by other users, and can be designed and

developed using arbitrary concepts. This includes that

we are not aware of the strategies performed by CM,

the goal provided by the corresponding user, and the

applied techniques, for instance. However, we can ob-

serve the external effects: i) the actions that are per-

formed by each a

and ii) the messages that are sent

and received.

Technically, a relationship between two agents

represents a functional connection. This means that

cooperation is required to solve a certain task: as

input-output relations, as (mutual) exchange of infor-

mation, or as negotiation between a group of a

, to

name just a few. In all these cases, interaction be-

tween agents takes place which we map onto the con-

cept of organisation: a

are connected functionally

with each other and these connections are dynamic.

We assume that establishing and changing re-

lations in technical systems requires communica-

tion. For simplicity reasons, we model commu-

nication as sending and receiving messages via a

(shared) communication channel. Conceptually, in-

direct communication methods such as stigmergy

(Beckers et al., 1994) can be mapped onto this com-

munication scheme. However, we neglect these cases

for the remainder of this paper. Most importantly, we

require that the medium is shared and messages are

routed using standard communication protocols and

infrastructure, e.g., popular mechanisms such as the

Transmission Control Protocol / Internet Protocol (IP)

tandem, see (Tanenbaum, 2002). Correspondingly, a

are uniquely identiﬁable (e.g., via their IP address).

Based on this communication model, we assume that

each message has an origin and a destination, and

there are no fake messages (i.e., from an attacker with

a modiﬁed origin ﬁeld). In addition, we require that

all messages are visible, and external sources (e.g.,

from users) can be identiﬁed (to neglect those mes-

sages as being not relevant for organisation).

3.2 Preliminary Work

In previous work (Kantert et al., 2015), we used a

variant of the aforementioned system model. We pro-

posed to measure the degree of organisation based

on the structure of communication and especially of

agreements in the system. To distinguish static or-

Measuring Self-organisation at Runtime - A Quantiﬁcation Method based on Divergence Measures

ganisation from dynamic self-organisation (i.e., as a

process returning the system from a disturbed state

into the target space in the sense of OC, see (Schmeck

et al., 2010)), we record and quantify changes in the

mentioned structure during and after disturbances oc-

cur in the system.

In order to estimate the degree of organisation,

three different communication graphs G

(p) = (V, E

)

are built. Each graph is generated for a period p be-

tween t

and t

. In all graphs, the set of vertices V rep-

resents the same set of agents in the system (i.e., each

agent represents an autonomous subsystem). How-

ever, the edges E

describe different kinds of commu-

nication processes in the system:

1. A graph G

contains edges for all possible com-

munication paths between nodes and serves as ref-

erence (i.e., it encodes the maximum of edges that

are possible).

2. A graph G

represents the observed communica-

tion, i.e., an edge is added if a communication be-

tween two nodes has been observed in the current

period. The edges E

in graph G

deﬁne a sub-

set of the edges in G

, since sending a message

requires a communication path.

3. In the third graph G

, edges represent mutually

stable relationships between two agents. In gen-

eral, relationships are temporary. Such a relation-

ship is the result of, e.g., a negotiation process.

Finally, the measure is deﬁned as:

Θ(G

, G

) :=

|{e

i, j

: e

i, j

∈ E

⊕ e

i, j

∈ E

0.5 ∗ (|V

| + |V

(1)

with G

as either G

or G

, E

deﬁning the set

of edges for the ﬁrst graph, E

the set of edges for

the second graph, V

and V

the corresponding sets of

vertices. We applied the concept to a scenario from

the smart camera domain, see (Rudolph et al., 2016).

Here, we showed that reorganisation effects can be

quantiﬁed using the developed metric. The graph cal-

culation and comparisons are done in three phases: 1)

at system startup, 2) during disturbances, and 3) af-

ter recovery from disturbances. This assumes distur-

bances to be seldom events that can be isolated and

detected appropriately fast. However, the approach

has some limitations—we will outline them and pro-

pose a modiﬁed technique in the next section.

4 AN APPROACH TO QUANTIFY

SELF-ORGANISATION

In this section, we initially discuss the limitations of

the previous approach, present a novel technique to

measure self-organisation in technical systems, and

discuss some design decisions related to this method.

Finally, we outline which challenges have to be ad-

dressed to apply the developed concept to real world

application.

4.1 Limitations of the Approach

The previously described approach (Section 3) is

characterised by some limitations:

1. It needs full knowledge about the underlying se-

mantics of the communication model. More pre-

cisely, we have to know if the message we observe

is related to system organisation aspects or not.

2. The approach assumes minimal communication,

i.e., agents do not share redundant information.

3. It assumes stable relationships between dis-

tributed entities in the overall system. More pre-

cisely, it builds a graph of nodes (reﬂecting en-

tities) and adds an edge if a relation exists, and

this relation is determined as result of an observed

communication.

In technical systems considered to be blackboxes (i.e.,

without access to internals), the required knowledge

about semantics may not be available (which is re-

lated to the ﬁrst drawback), individual agents may

broadcast data (which is related to the second draw-

back), or the communication may require a continu-

ous process (which is related to the third drawback).

This is accompanied by a possibility to detect mutu-

ally stable relationships for G

. Furthermore, self-

organisation may frequently result in changes of the

structure. The graph representation is an additional

limitation since it loses information: Either there is

an edge or not (and these edges are undirected). Self-

organisation processes may—in contrast to the as-

sumed handshake model for G

—require more so-

phisticated data exchange schemes, more complex

decision processes incorporating more than just two

partners, and come up with relations that involve more

than just two interaction partners. In turn, they may

also include directed relationships rather than undi-

rected. These cases are not covered by the approach;

the same holds for inherent dynamics (i.e., establish-

ing and closing down relationships more than once in

a cycle).

4.2 Modelling Self-organisation

In the following, we outline how these limitations are

overcome. We again assume that self-organisation

manifests itself by means of relations that are es-

tablished, updated, and released by communication.

ICAART 2017 - 9th International Conference on Agents and Artiﬁcial Intelligence

100

However, we do not require semantics or minimal

data load. To detect or measure the self-organised

behaviour of a technical system S, we observe the

communication behaviour occurring among the au-

tonomous agents a

We assume that a system S shows a “normal” com-

munication behaviour. This means that there are no

conspicuous communication patterns, and the com-

munication patterns are characterised by low dynam-

ics. As one example, we do not assume a minimal-

istic communication approach—but we assume that

for a certain context the same (or at least a very sim-

ilar) communication pattern will be used in all cases.

Expressed in a probabilistic framework, we repre-

sent each subsystem a

as a process that generates

observable samples (i.e., messages). When measur-

ing self-organisation (e.g., by means of sensors mon-

itoring the communication channels), we have to use

communication-speciﬁc pre-processing techniques to

extract the values of attributes (features) from those

samples (observations). These attribute values de-

scribe the current behaviour of the observed system.

For a standard message, at least origin, destination,

packet size, and time stamp will be available in the

header information of the package sent over the chan-

nel. Based on these perceived attributes, we model

the attribute space by a variable x in the following (or

x in the case of an one-dimensional attribute space).

In general, x may consist of categorical and continu-

ous attributes, for instance. Please keep in mind that

each message observed within a monitoring period is

one sample in our model.

The basic model of self-organisation suggested in

this paper is that the dynamics of the communication

patterns reﬂect the dynamics of the self-organisation

processes. If no self-organisation takes place (i.e.,

the structure of S is static) no communication for or-

ganisation purposes is required. There may be other

communication (i.e., messages) within the system,

but none related to structure adaptations. In response

to disturbances, changing external or internal con-

ditions, or modiﬁcations of the utility function (i.e.,

user-triggered or as a function of time), the system

structure may have to be adapted as well. This is as-

sumed to manifest in a change of the communication

pattern: Subsystems may start to communicate with

other systems, stop communicating with current part-

ners, or may change the message frequencies, to name

just a few implications. However, the basic point is

that something is different, without the need of know-

ing what is different at a semantic level.

Based on this idea, we deﬁne self-organisation as

an unexpected or unpredictable change of the distri-

bution underlying the observed samples (i.e., the com-

munication behaviour). Consequently, a divergence

measure can be applied to compare two density func-

tions. We will refer to a density function p(x) repre-

senting an earlier point in time and to q(x) as a density

function representing the current observation cycle. A

famous divergence measure is the Kullback-Leibler

(KL) divergence KL(p||q), see (Bishop, 2011). It is

deﬁned for continuous variables as follows:

KL(p||q) = −

p(x)ln

q(x)

p(x)

dx (2)

KL is sometimes referred to as relative entropy; how-

ever, there is also a discrete version of the measure,

see (Shannon, 2001). KL is known to be applicable

only in a restricted manner, since it is not symmetric.

If needed we can provide a symmetric measure using:

(p, q) =

(KL(p||q) + KL(q||p)) (3)

Although KL is still limited, it fulﬁls some important

requirements: 1) if p(x) = q(x) the measure KL(p||q)

is 0, and 2) KL(p||q) ≥ 0. Changing the formulation

of Equation 2 demonstrates the desired result:

KL(p||q) = −

p(x) ln q(x)dx+−

p(x) ln p(x)dx

(4)

This formula describes that we measure the expected

amount of information contained in a new distribu-

tion with respect to a reference distribution of sam-

ples. Taking the symmetric concept as deﬁned by

Equation 3 into account, we can adapt Equation 4 as

follows:

(p, q) =

(KL(p||q) + KL(q||p))

(−

p(x) ln p(x)dx −

p(x) ln q(x)dx

q(x) ln q(x)dx −

q(x) ln p(x)dx)

(5)

This formula (i.e., Equation 5) can be used as mea-

sure for quantifying self-organisation processes. Due

to the basic approach to compare distributions of the

underlying sample set (or more precisely: of the dis-

tribution of densities of observed samples within the

input space during a certain observation period), the

measure increases if the two distributions begin to

change. Considering the basic assumption we made

at the begin of this subsection, this exactly models

what we expect to observe if self-organisation takes

place.

The more subsystems a

participate in the struc-

ture building process, the higher is the divergence

Measuring Self-organisation at Runtime - A Quantiﬁcation Method based on Divergence Measures

101

to the previous distribution—and consequently, the

higher is the measured self-organisation. Systems

with hierarchical elements will be characterised by

different communication pattern, resulting in a de-

creased degree of self-organisation since external-

oriented (i.e., towards central components) messages

are neglected. In case of fully centralised sys-

tem structures, no self-organisation will be indicated:

Messages towards/from external units (i.e., the cen-

tralised components) are neglected, and the commu-

nication patterns among CM do not change (i.e., only

’normal’ behaviour in terms of “hello” messages, for

instance).

The most important advantages of this approach

are as follows: 1) Compared to, e.g., (Schmeck et al.,

2010) it does not require internal information (such

as the number of CM). 2) As an alternative to, e.g.,

(Muehl et al., 2007) it is continuously quantiﬁable. 3)

In comparison to, e.g., (Gershenson and Fernandez,

2012) it is independent of emergence and what is un-

derstood to be emergent behaviour. 4) In contrast to,

e.g., (Kantert et al., 2015) it is applied continuously

and not just for disturbed periods. 5) In contrast to

most of the concepts from Section 2, a general model

of how the system works is not necessary—it is appli-

cable with low effort. 6) In contrast to, e.g., (Shalizi

et al., 2004) it takes only attributes that are relevant

for the structure of technical systems into account. Fi-

nally, it can easily incorporate system boundaries by

specifying communication addresses.

4.3 Observation Cycles

The process as outlined before requires an inherent

comparability of two probability distributions. Trans-

ferred to the temporal behaviour of a self-organising

system, this implies that the potential self-organising

process manifests itself in the difference between a

current and a referential distribution of attribute oc-

currences. Expressed in the probabilistic approach as

outlined before, this means that we observe a num-

ber of processes that “generate” samples resulting in

probability distributions. For a comparison, we have

to deﬁne that the sample period is equal, i.e., we allow

the same time period for the current observations as

for a reference period. This can be done using a slid-

ing window approach: A ﬁxed time period d is used

to observe samples for the current estimation process

(i.e., between time t

and t

−1

) and the same duration

is used for a reference observation (i.e., the time pe-

riod directly before the current observations are done:

between t

−1

and t

−2

). Alternatively, the reference

window might be ﬁxed (i.e., static), e.g., at the be-

gin of the observation (here, slow changes can be de-

tected easier, but oscillating behaviour may be harder

to detect). Figure 2 illustrates both approaches. How-

ever, it may be beneﬁcial to use a hybrid approach

that combines both concepts: estimating the change

compared to the previous period and against a static

distribution to be able to cover all aspects.

time

relations

















Current

distribution

Reference

distribution 1























Reference

distribution 2

Figure 2: Two possibilities for choosing observation and

reference window: sliding and static window approach.

The duration of these windows has to be chosen

depending on the underlying application, i.e., the size

must be long enough to reliably estimate the probabil-

ity distributions and simultaneously short enough to

be able to consider the observations as being (almost)

time-invariant. However, there is no standard answer

of how to conﬁgure the window size. A good estimate

is the online self-adaptation cycle (i.e., the frequency

at which CM observes the system status and takes

decisions)—for instance, an organic system runs a

feedback loop deﬁned by the Observer/Controller tan-

dem in cycles of ﬁxed length to analyse the util-

ity of the currently applied action and decides about

necessary interventions accordingly (Tomforde et al.,

2011). Taking a period of k cycles into account may

serve as a ﬁrst starting point.

4.4 Open Challenges

This approach to quantifying self-organisation de-

scribes the general processes and the basic idea of

how self-organisation can be accessed. However, it

still comes with some limitations and open questions

that require research effort in the near future. From a

probabilistic point of view, we proposed to use KL as

divergence measure. This measure may take arbitrar-

ily high (positive) values. It would certainly be more

convenient to have a measure that is normalised, e.g.,

restricted to the unit interval [0; 1]. There are several

other divergence measures and we need to investigate

if one ﬁts better than KL.

As outlined before, the parameter d deﬁnes the

length of the window used to observe samples. Al-

ICAART 2017 - 9th International Conference on Agents and Artiﬁcial Intelligence

102

though choosing the length of d will depend on the

underlying application, the utilised communication

infrastructure, and the resulting communication pat-

terns, it may be beneﬁcial to search for a heuristic to

chose d. We already mentioned the adaptation cycle

of CM as a possible reference point.

Another issue is as follows: If all subsystems

come together in discrete cycles and decide about the

system structure in a broadcast-based all-to-all ap-

proach, our method would come up with no mean-

ingful results, since the distributions will be almost

identical. However, we can detect such a peak be-

haviour in the observation stream (even together with

the underlying period) and, consequently, identify a

system as a possible candidate for such market-based

self-organisation mechanisms.

5 EXAMPLE SCENARIO

To illustrate the presented technique, we outline a spe-

ciﬁc example application from the vehicular trafﬁc

control domain. However, the developed approach is

not restricted to a single domain. For instance, self-

adapting data communication networks are an obvi-

ous next step to analyse the behaviour of the mea-

surement, e.g., in the context of the system presented

in (Tomforde et al., 2009; Tomforde et al., 2010b).

Another possible application scenario to analyse the

behaviour in future work is a self-adapting activity

recognition system that dynamically includes sensors

from the environment and other devices as, e.g., out-

lined in (J

anicke et al., 2016). Here, the degree of

self-organisation can be used to quantify to which ex-

tent the system made use of its ability to include new

sensors or deactivate previously used sensors while

trying to maximise the recognition rate.

5.1 Scenario

Due to the dynamics of trafﬁc, adapting trafﬁc control

strategies to changing conditions is a promising appli-

cation area for self-adaptive and self-organising sys-

tems (Prothmann et al., 2011). Besides changing du-

rations of green phases, autonomous self-organisation

comes into play if intersection controllers (i.e., a

CM in the notion of Section 3.1) are responsible for

establishing and maintaining progressive signal sys-

tems (PSS)—also called “green waves”. In (Tom-

forde et al., 2008), a distributed PSS mechanism

(DPSS) for urban road networks is presented (Tom-

forde et al., 2008). The approach is a three step pro-

cess and works as follows: 1) Initially, distributed CM

determine partners that collaborate to form a PSS, 2)

after establishing partnerships, the collaborating CM

agree on a common cycle time, and 3) the partners se-

lect signal plans that respect the common cycle time,

calculate offsets, and establish a coordinated signali-

sation. We analyse this example in the remainder to

highlight the behaviour of the proposed measure.

For the ﬁrst step of DPSS, each CM estimates

(based on local sensor data) which is the most promi-

nent stream running over the controlled intersection,

i.e., the stream with the currently highest number of

vehicles

hour

. Afterwards, it sends a request for partnership

to the upstream CM—which is the desired predeces-

sor in a PSS. Either that CM accepts partnerships or

it rejects. In case of rejection, the second best neigh-

bour is asked. For the second step, an echo algorithm

is used that starts at the ﬁrst CM of a PSS. It estimates

the locally desired values for the cycle time and sends

this to the successor CM. All subsequent CM calcu-

late the maximum of this received value and their de-

sired cycle time and pass it to the next CM until the

last intersection of the PSS is reached. This last CM

propagates the chosen cycle time back to all CM in re-

verse direction. Finally, the ﬁrst CM selects the most

beneﬁcial signal plan (i.e., deﬁning green durations

at the underlying intersection) that reﬂects the deter-

mined cycle time, calculates an offset (i.e., a relative

start within the cycle) and passes this information to

its successor. This is continued until the last intersec-

tion is reached. When all CM activate their chosen

signal plan, the PSS is established. Afterwards, each

node continuously monitors if the trafﬁc behaviour

still corresponds to the desired PSS—and starts an

update or re-negotiation process if the preferences re-

garding trafﬁc streams or desired cycle time change,

or if a partner node is not available any more.

In this example, the organisation of the system

manifests itself in terms of functional relations by

means of forming a PSS, i.e., predecessor-successor

relationships. The system is self-organised with re-

spect to the deﬁnition in Section 3 since these rela-

tions are established and updated by the autonomous

CM participating in the system.

5.2 Analysis of the Behaviour

In this trafﬁc scenario, we assume each inter-

section controller (i.e., each CM) to continuously

send “hello”-messages to verify the availability of

neighbours—since a neighbour that is not reachable

via communication cannot participate in a PSS. In ad-

dition, the process itself requires communication ef-

fort in all three phases. This process runs continu-

ously: At system startup, initial coordination schemes

may be generated, and they are continuously moni-

Measuring Self-organisation at Runtime - A Quantiﬁcation Method based on Divergence Measures

103

tored and adapted throughout the system’s operation.

However, we observe periods of low communica-

tion effort (i.e., only “hello”-messages are exchanged)

where no self-organisation takes place. In this case,

the structure is static.

Trafﬁc load in urban areas changes during the

course of a day. As a consequence, the load on the

streams varies. Consider commuter trafﬁc as an il-

lustrating example: During the morning rush hours,

the highest trafﬁc load moves towards the city centre,

while the reverse direction is favoured in the after-

noon. Consequently, the best possible PSS switches

during lunch time from inwards to outwards. As a

conclusion from this simple example, we can observe

that the most prominent streams will change through-

out the day. As a consequence, the CM will even-

tually activate the DPSS mechanism with all three

phases, resulting in frequent message exchange. In

addition, this process is not necessarily a disturbance

as assumed in previous work. In contrast, it will most

probably happen frequently. However, in case of dis-

turbances (i.e., blocked roads and a resulting drop

in trafﬁc load for streams running over that road, or

failures of neighboured CM) we will observe com-

munication behaviour as well. The proposed mea-

sure is able to detect these phases of reorganisation

and consequently quantiﬁes the degree to which self-

organisation takes place in this example system.

As a basis of comparison, other concepts for PSS

can be compared to the DPSS approach using the

proposed metric. Systems with hierarchical elements

will show a different communication pattern, result-

ing in a decreased degree of self-organisation since

external-oriented (i.e., towards central components)

messages are neglected. In case of fully centralised

system structures, no self-organisation will be indi-

cated, since no messages among CM are exchanges

(besides “hello” messages, for instance).

6 CONCLUSION

In this paper, we deﬁned what self-organisation

means in technical systems from our point of view

and proposed a technique to measure and quantify

it at runtime. Our basic system model assumes au-

tonomous agents forming the overall system—which

means that we do not have any insights about the

status, the strategies, and the goals of an individual

agent. Consequently, we propose to base a measure

on the only information that is available for external

observers: the communication in terms of messages.

Compared to previous work, we do not make any

assumptions regarding the purpose and semantics of

communication. In contrast, we deﬁne a probabilistic

model to estimate distributions of samples (i.e., mes-

sages) within a ﬁxed time period. We then compare

the current distribution against a reference distribu-

tion. The more these distributions differ, the more

self-organisation takes place. We further discussed

how the sampling period to derive these distributions

has to be chosen and how a comparison can be calcu-

lated. For illustration purposes, we brieﬂy discussed

a scenario from urban trafﬁc control, i.e., establish-

ing progressive signal systems, and explained the ex-

pected behaviour of the proposed measure.

As part of this paper, we already discussed current

challenges to be addressed in Section 4.4. Our future

work will investigate how possible solutions can be

developed. For instance, we proposed to make use of

the Kullback-Leibler divergence to compare different

distributions. However, there are various divergence

measures known in literature and we have to inves-

tigate which performs best, i.e., quantiﬁes the effect

of self-organisation as close to human recognition as

possible.

Furthermore, the concept is based on the observa-

tion of communication—and the possibility to neglect

external messages (i.e., with origin or destination that

are not part of S). The developed measure may also

be used to relate it to the subsequent reorganisation

process. If knowing about external inﬂuences and ob-

serving reorganisation afterwards, it may serve as an

indicator that the system is less autonomous or that

the user triggered a change of utility. Consequently,

it may be extended towards estimating the autonomy

of the system at runtime. Given a long enough ob-

servation period, we may also be able to learn what

the most appropriate system structure is for a given

context (and a given utility function).

Finally, we aim at analysing the behaviour of

the developed measurement in simulations of self-

organised systems. Initially, we consider trafﬁc con-

trol as outlined before. Afterwards, we aim at increas-

ing the scope towards data communication and activ-

ity recognition systems.

ACKNOWLEDGEMENTS

The authors would like to thank the German

research foundation (Deutsche Forschungsgemein-

schaft, DFG) for the ﬁnancial support in the context

of the “Organic Computing Techniques for Runtime

Self-Adaptation of Multi-Modal Activity Recognition

Systems” project (SI 674/12-1).

ICAART 2017 - 9th International Conference on Agents and Artiﬁcial Intelligence

104

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