Formal infrastructure of multiagent system specified by
Agent UML and Petri Nets
Ph. D. Marijan KUNSTIC, B. Sc. Marina BAGIC
Department of Telecommunications, Faculty of Electrical Engineering and Computing
University of Zagreb
Zagreb, Croatia
E-mail: [email protected], [email protected]
ABSTRACT
“Softwaresation” of telecommunications and increasing
penetration of mobile agent technologies into
telecommunications has invoked research of well defined
techniques to validate and verify system specifications.
We present formal model for specification of multiagent
system using Agent UML language and Colored Petri Net
methods. Agent UML specifies system informally at all
levels of abstraction, but has no ability to either simulate
or verify system’s behavior. Colored Petri Nets offer this
major feature. Therefore, unification of Agent UML and
Petri net formalisms provides enough information on
system qualities. A lot of time and effort is saved in
further phase of system implementation. Increase in
system reliability is also significant. Colored Petri Nets
are extremely useful, and together with some of the other
modeling languages, e. g. AUML, they should be a
standard part of the repertoire of advanced system
designers and system analysts.
Keywords: Mobile Agent, Multiagent System, Formal
Specification, Agent UML, Colored Petri Nets
1.
INTRODUCTION
A multiagent system is a concurrent system based on the
notion of autonomous, reactive, and internally-motivated
agents in a decentralized environment [1]. To make it
possible for agents to communicate with each other, it is
essential for them to have a common communication
language and to follow common protocols. The
underlying agent communication model is usually
asynchronous, and an agent may decide whether to
perform actions requested by some other agents. Agents
are commonly designed to determine their behavior based
on individual goals, their knowledge and the
environment. They may autonomously and spontaneously
initiate internal or external behavior at any time.
2.
SPECIFICATION OF MULTIAGENT
SYSTEM BY AGENT UML
Here we use diagrams of Agent Unified Modelling
Language (AUML) to specify agent’s features and their
internal and external behaviours within a particular
multiagent system.
2.1. Mathematical model of Agent UML diagrams
2.1.1. Sequence diagram
Let us first define elements of formal infrastructure for
multiagent system. Definitions are given as in [4].
Definition 2.1. Sequence diagram is 5-tuple
SD := (I, P, M, O, A)
where I is a non-empty set of agents or agent roles. P is a
non-empty set of protocols where one is major (sd
Protocol), and the others can be either interleaved or
nested protocols. M is a set of messages either
synchronous or asynchronous. Each message is specified
as 2-tuple m := (a, options), where a  {as, aa}, as synchronous message, aa - asynchronous message, and
options specify whether a message is intended to be
received by more than a one receiver (n >= 1), or a range
of possible receivers ([m, n] equals m <= r <= n, where r
is a number of receivers). Also, an option can specify
some special conditions on which an message sending is
performed or to explicitly identify a particular agent. O is
a set of operators O := {alternative, option, break,
parallel, weak, strict, negative, critical, ignore, consider,
assertion, loop} such that can be easily extended to an
appropriate number of newly introduced operators. A is a
non-empty set of directed arcs connecting communication
actors, therefore it is A  I  I, and I  I is a set of (i1,
i2) for all i1, i2  I such that exists Cartesian product (i1,
i2)  I  I and is defined in A. Shape of arc must
correspond to character of message, thus arcs are either
synchronous or asynchronous.
:Initiator
:Participant
request
alternative
refuse
[refused]
[agreed and
notification necerassary] agree
alternative
failure
inform_done
 N is a complex number k1.k2...kn representing the
sequential order of the message within the next higher
level of procedural calling. Messages that differ in one
integer term are sequentially related at that level of
nesting.
Communication diagram can also be defined as
strongly connected directed graph where each node
represents communication actor of interaction and each
(virtually, two-headed) arrow represents relation between
two actors. Messages supplement arrows with semantics
of relation.
inform_result
2.1.5. Timing diagram translation
Figure 1. FIPA protocol for interagent communication in Telephone
exchange
2.1.2. Activity diagram
Definition 2.2. Activity diagram AD is 3-tuple
AD := (S, A, C)
where S is a non-empty set of agent states, A is a set of
relations between the states where A  S  S, and S  S
is a set of (s1, s2) for all s1, s2  S such that exists
Cartesian product (s1, s2)  S  S and is defined in A. C
is a set of conditions or events that decide whether agent
can change its state or not. These expressions are
represented as informal set of text strings.
2.1.3. Interaction Overview diagram
Definition 2.3. Interaction Overview diagram ID is 2tuple
ID := (SD, AD)
where SD is a set of interactions provided for interagent
communication as seen in sequence diagram, i.e. ID is a
collection of few sequence diagrams connected into one
diagram via AD, elements of activity diagram
Interaction Overview Diagrams focus on the
overview of the flow of control where the nodes are
Interactions or Interaction Occurrences. The Lifelines and
the Messages do not appear at this overview level [8].
Interaction Overview Diagrams are specialization of
Activity Graphs that represent Interactions, and differ
from Activity Diagrams in some respects.
Definition 2.5. Timing diagram
TD := (T, E)
Timing diagrams focus on conditions changing within
and among Lifelines along a linear time axis. Timing
diagrams describe behavior of both individual classifiers
and interactions of classifiers, focusing attention on time
of occurrence of events causing changes in the modeled
conditions of the Lifelines.
An example of each of the above defined diagrams can be
found in [4].
3.
COLORED PETRI NET APPROACH TO
MULTIAGENT SYSTEMS
Petri net is formally defined as [3];
Definition 3.1. A CP-net is a 9-tuple
CPN = (, P, T, A, N, C, G, E, I)
where is a finite set of non-empty colour sets, P is a
finite set of places, T is a finite set of transitions, A is a
finite set of arcs such that: P T = P A = T A = Ø,
N is a node function. It is defined from A into P TT
P. C is a colour function. It is defined from P into . G
is a guard function. It is defined from T into expressions
such that: t T: [Type(G(t)) = B Type(Var(G(t)))
]. E is an arc expression function. It is defined from A
into expressions such that: a A: [Type(E(a)) =
C(p)MS Type(Var(E(a))) ] where p is the place of
N(a). I is an initialisation function. It is defined from P
into closed expressions such that: p P: [Type(I(p)) =
C(p)MS]. The set of types determines the data values and
the operations and functions that can be used in the net
expressions (i.e., arc expressions, guards and initialisation
expressions).
2.1.4. Communication diagram
Definition 2.4. Communication diagram CD is 3-tuple
CD := (I, R, M)
where I is a non-empty set of agent identifiers (or agent
roles), R is a set of relations where R  I  I, and I  I is
a set of (i1, i2) for all i1, i2  I such that exists Cartesian
product (i1, i2)  I  I and is defined in R. M is a set of
messages where each message is represented as m :=
(k,,s) where s is a string value representing message name
or content of message in its simplest instantiation, and k
3.1. Petri nets benefits
CP-nets provide a framework for the design,
specification, validation and verification of systems. CPnets have a wide range of application areas, therefore can
also be applied in the area of network management. CPN
tools support the construction, simulation, and functional
and performance analysis of CPN models. CP-nets are
extremely useful, and together with some of the other
modelling languages (e.g. AUML, considered here), they
should be a standard part of the repertoire of advanced
system designers and system analysts. Some of CP-nets
properties are [3]:
• a well-defined semantics, which unambiguously
defines the behaviour of each CP-net;
• forms the foundation for the formal analysis
methods;
• generality which is to be used to describe a large
variety of different systems;
• very few, but powerful primitives;
• an explicit description of both states and actions;
• a semantics which builds upon true concurrency
instead of interleaving;
• hierarchical descriptions;
• integration of
the description of control and
synchronization with the description of data
manipulation;
• stability towards minor changes of the modelled
system;
etc.
3.2. Petri net based multiagent system
Problems to be solved for multiagent system specification
are, but not limited to:
•
•
•
•
•
•
•
•
conversation, or to continue with the current
conversation.
All communications between agents must be carried
out through asynchronous message passing as provided
by the MSP mechanism [1].
3.3. CASE STUDY: Telephone exchange
Case study to be discussed here is a simplified model of
telephone exchange realized by a set of agents:
•
•
•
•
•
•
Initialize_call_agent
Analyze_number_agent
Establish_call_agent
Establish_conference_agent
Disconnect_call_agent
Disconnect_conference_agent
Each agents has its own dedicated task which basically
corresponds to its name. At lower levels of abstraction we
decompose each agent’s task onto smaller or elementary
task (theoretical approach to be seen in [5]). As an
example Initialize_call_agent is to be decomposed to
tasks of checking the resources, checking the database
and checking black list of subscribers.
modular approach
common communication language
common protocols
asynchronous message passing
autonomous and internally-motivated agent
mental state
reasoning mechanisms
inheritance modelling.
To support agent-based design, we use extended G-net
model [1]. Five special modules are introduced to make
an agent autonomous and internally-motivated. They are
the Goal module, the Plan module, the Knowledge-base
module, the Environment module and the Planner
module. The template for an agent-based G-net model is
shown in Figure 5.
GSP(G)
Goal
Plan
Knowledge Environment
Manager
Incoming messages
request
refuse
confirm
Outgoing messages
info
info
request
refuse
confirm
Internal
activities
initialize call
Figure 3. Telephone exchange realizeed by G-net based agents
message
processing
MSP(self)
message
message
processing processing
MSP(self)
MSP(self)
message
processing
MSP(self)
message
processing
message
processing
message message check subscriber
processing processing
MSP(G'.Aid) MSP(G'.Aid) MSP(G'.Aid) MSP(G'.Aid)
return
Figure 2. Initialize_call_ agent as G-net based agent
A Manager module is the heart of an agent that may
decide to ignore an incoming message, to start a new
According to agent-based Petri net model [1] we
visualize generic model for interagent communication
and internal methods for Initialize_call_agent (Figure).
Incoming and outgoing messages represent agent’s
communication with other agents. Internal activities
correspond to agent’s internal structure and possibilities
of dynamic behavior. Modules Goal, Plan, Knowledge
and Manager are based on BDI agent model (to be seen
in [1]) and correspond to agent formal specification.
translated onto arc expressions. Set of messages M are
also translated onto arc expressions and tokens moving
from one place to another.
4.2. Communication diagram translation
Communication diagram CD := (I, R, M) is translated
onto Petri places and transitions by creating a collection
of these for each agent identifier from I set. There is no
explicit mechanism to represent R, a set of relations.
Thus, it is expressed via connection between various
places of each of agents involved. M, a set of messages is
translated via Petri arc expressions and also tokens
chosen to carry information between Petri entities.
Figure 4. Initialize_call_ agent task decomposed to elementary tasks
4. TRANSLATION MECHANISM FROM AGENT
UML ONTO COLORED PETRI NETS
4.1. Sequence diagram translation
Translation of set SD := (I, P, M, O, A) toward Petri net
concepts sets I, set of agents in a collection of Petri places
and transitions. Here, the main issue is to recognize
WHAT is to be represented by Petri places and
transitions, the communication itself of entities involved
in the particular communication. P, protocols are
4.3. Activity diagram translation
Activity diagram AD as (S, A, C) is inherently closest to
genuine Petri net concept where S is a non-empty set of
agent states, A is a set of relations between the states
where A  S  S, and S  S is a set of (s1, s2) for all s1, s2
 S such that exists Cartesian product (s1, s2)  S  S and
is defined in A. C is a set of conditions or events that
decide whether agent can change its state or not. These
expressions are represented as informal set of text strings.
4.4. Timing diagram translation
Timing diagram TD := (T, E)
Timing diagrams focus on conditions changing within
and among Lifelines along a linear time axis. Timing
diagrams describe behavior of both individual classifiers
and interactions of classifiers, focusing attention on time
of occurrence of events causing changes in the modeled
conditions of the Lifelines.
Figure 5. Implemention of agent communication
4.5. Simulation results
Results of Petri net simulation are imported in a state
space file which is generated automatically. It is shown in
a form of table below.
Occurrence Graph
•
Nodes: 8
•
Arcs: 10
FIPArequest'InitInfoRes 1
FIPArequest'InitRequested 1
FIPArequest'PartAgreed 1
FIPArequest'PartFailed 1
FIPArequest'PartInfoDone 1
FIPArequest'PartInfoRes 1
FIPArequest'PartRequested 1
Best Upper Multi-set Bounds
FIPArequest'InactiveInit 1
FIPArequest'InactivePart 1
FIPArequest'InitAgreed 1
FIPArequest'InitFailed 1
FIPArequest'InitInfoDone 1
FIPArequest'InitInfoRes 1
FIPArequest'InitRequested 1
FIPArequest'PartAgreed 1
FIPArequest'PartFailed 1
FIPArequest'PartInfoDone 1
FIPArequest'PartInfoRes 1
FIPArequest'PartRequested 1
Scc Graph
•
Nodes: 1
•
Arcs: 0
Home Properties
• Home Markings: All
Liveness Properties
• Dead Markings: None
Boundedness Properties
Best Integers Bounds
• FIPArequest'InactiveInit 1
• FIPArequest'InactivePart 1
• FIPArequest'InitAgreed 1
• FIPArequest'InitFailed 1
• FIPArequest'InitInfoDone 1
•
•
•
•
•
•
•
Upper Lower
1
0
2
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1`request
1`request++1`tag
1`agree
empty
empty
1`inform_result
1`request
1`inform_result
empty
empty
1`inform_result
1`agree
Dead Transitions Instances
•
FIPArequest'Failured 1
•
FIPArequest'InformDone 1
•
FIPArequest'InitDoneRet 1
•
FIPArequest'InitReturn 1
•
FIPArequest'PartDoneRet 1
•
FIPArequest'PartReturn 1
•
FIPArequest'Return 1
Live Transitions Instances
•
FIPArequest'Agree 1
•
FIPArequest'InformResult 1
•
FIPArequest'InitRequest 1
•
FIPArequest'InitResRet 1
•
FIPArequest'PartResRet 1
•
FIPArequest'RepRequest 1
Fairness Properties
•
FIPArequest'Agree 1
•
FIPArequest'Failured 1
•
FIPArequest'InformDone 1
•
FIPArequest'InformResult 1
•
FIPArequest'InitDoneRet 1
•
FIPArequest'InitRequest 1
•
FIPArequest'InitResRet 1
•
FIPArequest'InitReturn 1
•
FIPArequest'PartDoneRet 1
•
FIPArequest'PartResRet 1
•
FIPArequest'PartReturn 1
•
FIPArequest'RepRequest 1
•
FIPArequest'Return 1
Impartial
Fair
Fair
Impartial
Fair
Impartial
Impartial
Fair
Fair
Impartial
Fair
Impartial
Fair
TABLE 5.1. OUTPUT FILE REPORT OF PETRI NET SIMULATION
The above statistics show respectively;
The first part of the state space report contains some
statistical information about the size of the state space in
notions of graph nodes and arcs.
The integer bounds give us information about the
number of tokens, while the multi-set bounds give us
information about the values which the tokens may carry.
A home marking is a marking which is reachable
from all reachable markings. A dead marking is a
marking with no enabled transitions.
Fairness properties provides information on how
often the individual transitions occur. Impartial means
that each of them occurs infnitely often in any infinite
occurrence sequence. Fair is a weaker fairness property
stating that the transition occurs infinitely often in all
infinite occurrence sequences where it is infinitely often
enabled [2].
5. CONCLUSION
In this paper we have offered formal model for
specification of mobile agents in telecommunications
systems. We’ve presented the “infrastructure” for formal
presentation of agent model as problem solving agent.
Hence we’ve defined problem environment, problem
space and problem set as well as solver vector space and
set of problem solvers.
We have also research on mechanism of translation
from specification to implementation of agent system and
object-oriented techniques were found suitable to easily
transform vectors to objects.
Major aspect of system development is to ensure
system is robust and reliable. Therefore it requires welldefined formal system specification and proper validity
and verification methods. Here wide area of research on
system specification and design arises. According to
agent-oriented model respected multiagent system must
support agents features such as autonomy, reactiveness
and internal motivation. Colored Petri nets provide a
framework for the design, specification, validation and
verification of systems. They support the construction,
simulation, functional and performance analysis of CPN
models. CP-nets together with modeling language, e.g.
AUML, should be a standard part of the repertoire of
advanced system designers and system analysts
6.
REFERENCES
H. Xu, and S. M. Shatz, A.B. Smith, “A framework for ModelBased Design of Agent-Oriented Software”, IEEE Transactions on
Software Engineering, Vol. 29, No. 1, 2003.
[2] L. M. Kristensen, S. Christensen, K. Jensen, “The practitioner’s
guide to Coloured Petri nets”, IEEE Transactions on Software
Engineering, Int J STTT 2, Springer-Verlag, 1998., pp. 98-132.
[3] K. Jensen, “An introduction to the Theoretical Aspects of
Coloured Petri nets”, A Decade of Concurrency, Lecture Motes in
Computer Science vol. 803, Springer-Verlag, 1994., pp. 230-272.
[4] M. Kunstic, M. Bagic, “Verification and validation of multiagent
system specified by Agent UML”, 1st International Conference on
Information & Communication Technologies from Theory to
Applications – ICTTA ’04, Damascus, Syria, 19–23 th April 2004.
[5] M. Kunstic, M. Bagic, “Development of formal infrastructure for
perception of intelligent agents as problem solvers”, International
Conference on Computer, Communication and Control
Technologies CCCT ‘03, Proceedings Volume 3 Computer,
Communication and Control Technologies, IIIS, Orlando, Florida,
USA, July 31 – August 2 2003., pp. 65-69.
[6] M. Kunstic, O. Jukic, M. Bagic, “Definition of formal
infrastructure for perception of intelligent agents as problem
solvers”,
International
Conference
on
Software,
Telecommunications and Computer Networks Softcom 2002.,
FESB, Split-Dubrovnik, Venice-Ancon, October 8-11, 2002., pp.
9-12.
[7] S. S. Alshir, “UML in a nutshell”, O’Reilly & Associates, Inc.,
1998.
[8] Object Management Group, Unified Modeling Language (UML)
Specification: Infrastructure, ptc/03-09-15.
[9] K. Jensen, “An introduction to the Practical Use of Coloured Petri
nets”, Advanced Course on Petri Nets, Dagstuhl, Germany, 1996.
[10] R. Pooley, P. King, “Derivation of Petri Net Performance Models
from UML Specifications of Communications Software”,
Proceedings of the fifteenth annual UK Performance Engineering
Workshop, July 1999., pp. 45-56.
[11] F. Bergenti, A. Poggi, “Exploiting UML in the Design of MultiAgent Systems”, Lecture Notes in Computer Science, In A.
Omicini, R. Tolksdorf and F. Zambonelli, Engineering Societiea
in the Agents World, Springer, 2000., pp. 106-113.
[12] P. Hughes, A.; Pahl, C., “A Generic Model for State-based Agent
Systems”, Proceedings of the 1st Irish Workshop on Formal
Methods, Dublin, 1997.
[1]