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International Journal of Multimedia Technology Jun. 2013, Vol. 3 Iss. 2, PP. 38-44
© American V-King Scientific Publishing
- 38 -
A Coloured Nested Petri Nets Model for Discussing
MANET Properties
Alessandro Bianchi 1, Sebastiano Pizzutilo 2
Department of Informatics, University of Bari via Orabona, 4 - 70125 Bari - Italy
1 alessandro.bianchi@uniba.it; 2 sebastiano.pizzutilo@uniba.it
Abstract- Predicting behavior and assuring quality of service of
complex multimedia systems is very hard. Techniques based on
tests, inspections or simulations are not always effective.
Conversely, rigorous adoption of formal approaches in entire
system lifecycle is very costly, and does not provide evidence
about run-time performance. Our research proposes a tool,
which allows both formally modeling and simulating a Mobile
Ad-hoc NETwork - MANET. Previous paper of same authors
discussed the tool effectiveness in simulating the system; the
present paper deals with the Petri Nets-based model of
MANET behavior, and shows the model usefulness in
predicting some interesting computational properties.
Keywords- MANET; Coloured Nested Petri Nets; Formal
Models; Complex Distributed Multimedia Systems;
Computational Properties of Systems
I. INTRODUCTION
Development of complex software systems involving
several modules, often distributed across different sites and
architectures, and treating several media is an error prone
process; discovery of possible weakness is hard and
sometimes very costly. Roughly speaking, in order to face
this issue, two main different approaches are usually
adopted: the verification approach, aimed at establishing
requirements fulfillment through some formal proof, and the
validation approach, evaluating the goodness of products
through simulation and testing.
Both of them present disadvantages: formal verification
is quite difficult, requires deep skill and consumes large
amount of effort, without allowing performance measures;
validation techniques are often unable to discover defects,
so they cannot guarantee high quality. The thesis we
propose in our research states that proper models of systems
are very useful in evaluating a number of properties. More
precisely, if the desired system is abstractly represented
before its development, those properties can be easily
studied through analysis on the model. The consequent,
rigorous implementation of the model allows guaranteeing
the satisfaction of desired quality of service in the target
system, so its possible weakness is overcome in advance.
In order to provide evidence to thesis above, this paper
discusses the usefulness of a Petri Nets-based model for
studying some interesting properties in Mobile Ad-hoc
NETworks (MANET). A Mobile Ad-hoc NETwork is a
network designed for wireless multimedia communications
among nomadic hosts; it does not need any fixed
infrastructure, and communication sessions between source
and destination are established and maintained by the
cooperation of hosts in the network. To this end, each host
plays a twofold role, acting as both data producer /
consumer and packets router [1].
The twofold role played by hosts in the network (end-
point of a communication session, and intermediate router)
and the continuous change of network topology due to
movement pose a number of issues: definition of specific
routing protocols and services for properly manage the lack
of fixed infrastructure; study of performance; specification
of resources allocation policies; analysis of problems related
to synchronization, concurrency and cooperation, and so on.
Literature discusses these issues, from different points of
view, in most cases with the support of tools simulating the
network behavior. Among them, the most largely adopted
are the “Network Simulator ns-2” [2], and its extensions, for
example “Monarch” [3]. This approach is very effective,
mainly for evaluating performance and comparing different
solutions, but they are not able to formally model MANETs.
In other words, these tools are just simulators: they
implement the network at a low abstraction level, but they
cannot support specification at a higher level, so, analyzing
typical features of mobile systems is hard. Conversely, some
papers formally model MANET, but they do not allow
analyzing and measuring run-time performance.
In order to overcome these problems, we developed the
prototype of moDEling MObile NEtworks (DEMONE). In [4]
we showed that DEMONE is able to simulate MANET
behavior as well as other simulators: DEMONE has been
applied to 3000 simulations and the results it obtained are
analogous to the findings reported in literature and obtained
using different simulators. Moreover, DEMONE allows the
formal description of MANET through Petri Nets, so it can
be used for specifying MANETs protocols and services as
well as for studying performance. The present paper focuses
the PN-based model of MANET and discusses its ability to
analyze some interesting computational properties.
In the following, Section II introduces the background
about Petri Nets; Section III provides an abstract view of
MANET; Section IV briefly depicts the PN-based model of
MANET, whose properties are discussed in Section V;
Section VI concludes the paper with a comparison of our
research to main results in literature.
II. BACKGROUND ON PETRI NETS
A. Generality
Petri Net (PN) is a conceptual tool, particularly suitable
for modeling dynamic and transitional systems [5]. A PN is a
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© American V-King Scientific Publishing
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recursive transition diagram, in which places (denoted by
circles) and transitions (denoted by boxes) are the nodes,
linked each other by arcs; each place can contain zero, one
or more tokens (denoted by dots). Arcs link places to
transitions and transitions to places, i.e., no place is directly
linked to another place, and no transition is directly linked
to another transition. The marking of a place, i.e. the
number of tokens contained in it, represents the current state
of the modeled system; transitions represent the
computational activities carried out by the system when it
changes its state.
Formally, a PN is a 7-ple: PN=<N, P, T, A, SP, EP, M>:
• N is the name of the net; P is a finite, non-empty set
of places: p1, p2, ..., pn;
• T is a finite, non-empty set of transitions: t1, t2, ..., tm;
• A is a finite, non-empty set of oriented arcs linking
elements in P to elements in T or elements in T to elements
in P, i.e., A: (P X T) ∪ (T X P) {0, 1};
• SP ⊆ P i s the subset of P i d enti f yi n g the starting
places; EP ∈ P is the unique end place;
• M is the marking function, M: P ℕ.
For each transition t, its preset (Pr(t)) is the set of places
incident on t, i.e., ∀p ∈ P, ∀ t ∈ T, p ∈ Pr(t) ⇔ A(p, t) =
1, and the postset of t (Po(t)) is the set of places following t,
i.e., ∀p ∈ P, ∀ t ∈ T , p ∈ P o (t) ⇔ A(t, p) = 1.
A transition t is enabled when its preset is marked; if so t
can fire, i.e., the associated computational activities can be
executed. After t fires, the number of tokens in its postset
increases and the number of tokens in its preset decreases
accordingly, i.e., the PN changes its state.
B. Coloured-Nested PNs
In order to model hierarchical tasks in processes the PN
formalism has been enriched by “nesting”. In a Nested Petri
Net (NPN), a labeling function L is associated to transitions:
this function maps each transition into the name of another
PN, or into NIL; if L(t) ≠ NIL, t is a nested transition.
Labeling transitions enables the designer to directly model
hierarchical task: the general structure and topology of a net
is specified starting from the top-level task, and subtasks are
described by calling a new subnet.
Colours can be employed to specify a place-conditioning
function, so allowing to specify “conditions” on the state of
the net. This can be represented by ‘colouring’ the marking
function of the PN. So, a Coloured Nested Petri Net (CNPN)
is formally defined as CNPN = < N, P, T, A, SP, EP, M, L,
Φ>, in which:
• N, P, T, A, SP, EP are defined as in basic PNs;
• the marking function is M: P -> Φ , where Φ is a set
of token colours;
• L is the labeling function.
Differently coloured tokens denote distinct contexts in
which the system might be employed. The CNPN formalism
is in our opinion sufficient to model a MANET.
C. Properties
The usage of PNs for specifying the dynamic behavior
of a system enables the analysis of some properties, which
are particularly interesting from a computational point of
view. If we consider tokens as data, or, more in general,
resources, a place can be seen as the location where tokens
reside; in other words, a place is a temporary or persistent
data storage, either containing a variable or a constant
number of tokens at any time. The dynamic behavior of a
PN is controlled by the movement and propagation of
tokens. So, the placement of tokens at the beginning of
execution allows predicting some features of both the PN
and the modeled system.
More precisely, given the initial marking M0 of a PN,
the following properties can be analyzed.
Reachability of a marking Mi: Mi can be reached since
M0 if a sequence of transitions exists such that the marking
M0 is transformed in the marking Mi; if a marking is not
reachable, then the transitions it drives are useless.
Liveness of a transition tj: if for all markings Mi
reachable from M0, there is a firing sequence from Mi which
contains tj; liveness guarantees absence of deadlock.
Reversibility of a PN: for all markings Mi reachable
from M0, then M0 is reachable from Mi; it indicates a cyclic
behavior of the system.
k-boundedness of a PN, i.e. for all markings Mi
reachable from M0, the number of tokens in each place is
never greater than k; boundedness implies the absence of
resource overflow in the system.
Conservativeness of a PN, i.e., for all markings Mi
reachable from M0, the total number of tokens does not
change; conservativeness means the invariant need of
resources.
III. ABSTRACT VIEW OF MANET
Nodes in a MANET communicate through wireless
channels, without any predefined physical infrastructure.
They are autonomous agents and they can dispose without
according to a predefined topology. During their lifetime,
hosts enter or leave the network, and continuously change
their relative position, so the network must quickly adapt to
changes. The system itself is the unique responsible of setup,
communication management and adaptation [1].
At a first glance, a MANET can be considered as a set of
one or more hosts, therefore, modeling a MANET means
modeling a number of hosts. Each host directly
communicates with all other hosts within the area
established by its transmission range; communications to
hosts external to this area need the contribution of
intermediate hosts.
Moreover, each host is a computational agent, which
plays two different roles. On one hand, it behaves as a
mobile agent, and therefore it moves at some speed,
following a direction; due to movements each host can go
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outside the MANET space, i.e. it can go in a place where it
cannot communicate to any other host. On the other hand,
each host is a communicating agent, so it starts a
communication session to a destination, acting as an
initiator; or it is destination of a communication; or it can be
involved in activities aimed at establishing routing,
according to the adopted protocol. In order to simplify
simulations, in DEMONE we require that a host, which is
an initiator/destination of a communication session CSi
cannot be initiator/destination for new sessions until end of
CSi. Instead, it can be involved as intermediate router in
several sessions. It is worth noting that the simplification
induced by this requirement does not reduce generality of
our approach: the requirement can be easily relaxed by
simple changes in the model and in the consequent
implementation.
More abstractly, communication activities executed by
hosts are represented by a number of services offered both
to users and to other hosts. Typical examples are local or
remote execution of multimedia application, routing
activities according to the adopted protocol, discovery of
services provided by other hosts, and so on: more in general,
all of them represent the building blocks of a Service
Discovery Protocol Framework [6].
In order to show an example of a service, we focus one
of the most popular routing protocol [7]: Dynamic Source
Routing (DSR). DSR is specified as Internet draft [8]. All
nodes record into a cache the known recent routes to other
nodes. If an initiator intends send a message to a destination,
it searches into its cache if a route to destination is known. If
so, the algorithm ends and the communication session can
start following that route. Otherwise, if destination is one of
initiator's neighbors, i.e., it is within its transmission range,
then a direct communication starts, and the protocol ends.
Otherwise, initiator delegates all its neighbors to find the
route, and each of them reiterates the previous process. To
this end, the initiator broadcasts a route request (RREQ)
packet to all its neighbors, which contains: its identifier; the
identifiers of initiator and destination; the list of the
identifiers of nodes it encountered since its creation, which
represents the route followed by the RREQ. Nodes receiving
RREQ interpret it, and execute one of the following.
Action 1: Route reply. If it is the destination, then it stops
RREQ, creates a route reply (RREP) packet containing the
route followed by RREQ, and unicasts RREP back to the
initiator, following the discovered route. When the initiator
will receive RREP, communication session starts.
Action 2: Discarding RREQ. If the node receiving RREQ
recently processed another RREQ from the same initiator
and directed to the same destination, or if the node finds that
its own identifier is already listed in the route recorded in
RREQ, that RREQ is discarded because it followed a loop.
Action 3: Broadcasting RREQ. If no one of previous
holds, then the node appends its identifier to the list in RREQ,
and broadcasts the new RREQ to all its neighbors.
IV. THE MODEL
For the purposes of present work only main features of a
MANET system are considered, so we can abstract some
issues, which are fundamental in real MANET, for example
transmission range [9], efficient power consumption [10],
direction and speed of movement, and so on.
The abstraction depicted in previous Section allows
structuring hierarchically the MANET (Fig. 1); the
hierarchy is then modeled using CNPN.
Fig. 1 The structure of the model
MANET PN is at the highest layer: it comprises the
existing hosts and establishes the intention of starting
communication sessions. Each host is represented at Layer 1
by a PN (named HOST PN). The two main aspects of hosts’
behavior (movement and communication) are described at
next layer by MOBILITY PN and COMMUNICATION PN,
respectively. The former does not present further details; the
latter includes PNs for providing communication services,
routing protocols, and so on. It is worth noting that
movement and communication are not related: hosts can
move even if they are outside MANET space, instead
communications can happen only when the hosts are inside
that area. Depending on the specific service executed, each
one of the SERVICE PNs at Layer 3 can be detailed in one
or more nested PNs.
For space reasons in the following only the most
meaningful PNs are described. With respect to usual PN
notations introduced in Section II, in following figures:
transitions with more detailed, nested descriptions are
represented by boxes with a small inner box in the bottom-
right corner; the types of tokens allowed in a place are
expressed as label near the place; if the preset or the postset
of a transition includes places belonging to PN at different
level, then “In” or “Out” label appears near the place,
respectively.
Every time a new host is added to the MANET, one
HOST token is produced in MANET PN at higher layer, and
therefore a new instance of a Host PN is created in Layer 1:
this PN is shown in Fig. 2.
This PN includes four types of tokens: HOST,
establishing the existence of that host inside the MANET
space; MOBILE, stating the ability of host to move;
FAILURE, signaling some operation failed so recovery is
needed; and SEND, showing whether the host can
send/receive packets. MOBILITY transition can be always
fired, i.e. its preset always contains a MOBILE token; when
this transition fires the host moves. Instead,
COMMUNICATION transition can be fired only if
MANET place contains a HOST token, and if HOST
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READY place contains at least one SEND token. Execution
of COMMUNICATION transition moves one SEND token
to PCK SENT place. Tokens in MANET and HOST
READY places are produced by the upper layer. Remaining
places (SWITCHING HOST ON/OFF and OUTSIDE) and
transition (EXCEPTION) are used for
activation/deactivation of hosts and for handling exception
during execution.
Fig. 2 Host PN
During each communication session, a host can act as
initiator, intermediate router, or as destination of packets:
these roles are detailed by Communication PN nested into
COMMUNICATION transition. The specific behavior of
hosts in each role strictly depends on several factors: the
specific service executed, the adopted routing protocol, and
so on. For example, Fig. 3 shows the PN describing the
behavior of an initiator when DSR protocol is used.
Fig. 3 DSR Initiator PN
This PN includes HOST tokens and SEND tokens, but
each place can contain only 0 or 1 token of any type. In this
way the requirement establishing the inability to start new
communications until end of the current one is satisfied. In
fact, if the host starts the ROUTE REQUEST transition, its
preset loses the unique SEND token, this place can be
marked again only after communication completion.
Analogous considerations hold for the PN representing hosts
acting as destination.
Fig. 4 DSR route request PN for intermediate router
Instead, when a host behaves as intermediate router, it
can be involved in two different activities: searching route
to destination, so processing RREQ packets (Fig. 4), or
communicating back found route to initiator, so processing
RREP packets (Fig. 5). In both cases the PNs include 0, 1,
or more SEND tokens, depending on the total number of
communication sessions it is currently serving.
Fig. 5 DSR Route Reply PN for Intermediate Router
V. DISCUSSION
The CNPNs summarized above allows discovering some
interesting features of the MANET system implemented
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according to them: in other words, if the MANET is
developed according to that model, then we can state it will
be characterized by the features corresponding to the
properties.
Due to the layered, nested structure of the model, the
analysis of properties should be executed for each PN
separately. Nevertheless, for most properties the obtained
results are always constant for all PNs, so for space reasons
we only report the results, without entering the details; only
boundedness and conservativeness present different results
in different layers, so they require more detailed discussion.
In general, we can note that for all layers all markings are
reachable, so, all transitions in all PNs can be fired, and
therefore all computational activities associated to those
transitions can be executed. This means that conditions exist
for executing all the logical components of all the algorithms
implementing the system and the offered services, at any
layer.
Secondly, each transition in all PNs is at least contained
in a path connecting the initial marking to each other
marking, therefore liveness property is satisfied. As a result,
all algorithms can be executed without risk of deadlock.
Reversibility is not always satisfied. More precisely,
when a host executing some algorithms (for example,
producing or consuming data packets, or routing them to
proper destination) moves outside the MANET space the
communication session fails. In order to properly manage the
recovery of the failed algorithm the control is taken by a
specific module, modeled by the Exception PN in Fig. 2.
In a MANET, several hosts can participate several
communication sessions simultaneously, and during
MANET lifetime, the number of hosts can vary
continuously. Therefore, in the highest layer both the
number of tokens establishing the existence of a host in
MANET space and the number of tokens establishing the
ability to send/receive packets can vary during execution. So,
MANET PN is unbound with respect to both HOST token
and SEND token. As a result, boundedness is not satisfied
for MANET PN, and therefore it is not conservative.
Each Host PN in Layer 1 is 1-bound, for HOST token,
but it is unbound for SEND tokens. In fact, one HOST token
is added/removed, depending on entrance/exit of
corresponding host in the MANET space; so there is not
conservativeness for this type of token. Instead, each place
in Host PN can include 0, 1 or more SEND tokens,
depending on the needs established by upper layer, and on
the role played by the host with respect to the
communication session. So, the total number of SEND
tokens can increase indefinitely, and consequently, Host PN
is unbound and not conservative with respect to SEND
tokens. Moreover, each host can always move, in fact one
and only one MOBILE token is always present. So this PN
is 1-bound and conservative with respect to this token.
Finally, a failure can happen at any time, so at most one
FAILURE token can be created in any time. Therefore, Host
PN is 1-bound and not conservative with respect to this
token.
Both 1-boundedness and conservativeness are inherited
by Mobility PN and Communication PN in Layer 2. Both
PNs receives tokens by Layer 1 and no token is
added/removed during execution.
In lower layer, both boundedness and conservativeness
strictly depends on the specific service and on the role
played by the host in providing that service. For example,
due to the requirement concerning the ability to participate
only one communication session per time, if the host is the
initiator/destination of DSR protocol, the corresponding PNs
are 1-bound for both HOST and SEND tokens;
conservativeness is satisfied with respect to HOST token,
but it is not satisfied for SEND token. In fact, this token is
removed after sending message. On the opposite, if the host
acts as an intermediate router, both when processing RREQ
and RREP, the corresponding PNs are unbound, and
conservativeness is not satisfied.
VI. COMPARISON TO LITERATURE AND CONCLUSIONS
The need to evaluate and analyze behavior of MANET is
acknowledged by large literature. In many cases the study is
executed with the support of simulators. Thanks to them
many results in MANET literature have been discovered,
confirmed or rejected. For example [11], [12], [13], [14],
and [15] compare some routing protocols performance; [16]
studies congestion adaptive routing; [17] discusses the
difficulties in managing synchronization among components
involved in simulation. Nevertheless, some authors (e.g.
[18], [19]) show that sometimes the results obtained using
simulators are inaccurate or poorly reliable.
On the other hand, some papers develop formal analysis
of MANET system. Among them, some extensions of Petri
Nets are often used, for example: [20] develops a High
Level Petri Nets model for specifying network layer
protocols for location service and for position-based routing;
[21] adopts Stochastic Petri Nets for analytical modeling of
a policy distribution architecture; [22] uses Stochastic Well-
Formed Petri Nets for limiting the number of call
connections. Colored Petri Nets are adopted by [23] for
modeling DYnamic MANET On-demand (DYMO) routing
protocol.
All works above focus just one of the two main issues in
complex systems research, i.e. they measure some metrics
for establishing the most adequate solution from an
execution point of view, or they formally model the system
for studying its behavior from a more abstract point of view.
The tool DEMONE [4] faces both issues of formally
modeling the system and evaluating its performance. In this
sense our approach is similar to [24] that uses Colored Petri
Nets for modeling Ad-hoc On-demand Distance Vector
(AODV) routing protocol, and moreover it simulates
MANET behavior according to the CPN model. The main
difference concerns the general-purpose view of DEMONE,
in which routing protocol is just one of the provided
services. In fact, each intended service can be modeled in
our layered framework, and implemented in simulator.
Thanks to the nested approach, services can be easily added,
removed and replaced by changing some transitions and
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nested PNs, as well as changing classes in software
implementation.
Moreover, thanks to the formal modeling, some
interesting computational properties of the obtained PNs are
discussed, and the consequent implementation guarantees
the correctness of MANET behavior. It is worth noting that
the experience gained in the present work provides first,
preliminary evidence of usefulness of formal modeling in
development of complex systems. In fact, the strict, rigorous
implementation of the PNs allowed avoiding deadlock and
redundancy of logical components: we can ensure these
features thanks to the satisfaction of liveness and
reachability properties, respectively. The analysis of
boundedness and conservativeness guarantees the
satisfaction of the requirement concerning the ability to
participate only one communication session per time.
Development of our research is currently dealing with
the usage or different formal models, for example in [25] a
preliminary model based on Abstract State Machine - ASM
[26] has been applied for studying some aspects of Grid
systems. The long-term purpose of our investigation is to
define a model of impact of different formal models with
respect to different applications in complex distributed
multimedia systems.
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Alessandro Bianchi graduated in Computer
Science at University of Milano and obtained
a PhD in Information Engineering at
University of Brescia. He currently is an
Assistant Professor at the Computer Science
Department of University of Bari. His
research interests deal with application of
formal models and methods in complex
distributed systems.
Sebastiano Pizzutilo is an Associate
professor at the Computer Science
Department of University of Bari since 2001.
His research activities concern network
protocols, distributed systems, multi-agent
theory and languages, formal methods for
evaluating user-adapted interfaces and
computer architecture. Prof. Pizzutilo
participated and coordinated several European,
national and local research projects about
these topics.
