MODEL-BASED STOCHASTIC SIMULATION OF SUPER PEER

PROMOTION IN P2P VOIP USING GRAPH TRANSFORMATION

Ajab Khan and Reiko Heckel

Department of Computer Science, University of Leicester, Leicester, U.K.

Keywords:

Stochastic modelling and simulation, P2P VoIP, P2P VoIP network architecture, Graph transformation.

Abstract:

The concept of super peer has been introduced to improve the performance of popular P2P VoIP applications.

A super peer is the strongest peer in the network that has the capacity to act as a server for a set of VoIP clients.

There is no doubt that by taking beneﬁt of heterogeneity, super peer can do improve the efﬁciency, without

compromising the decentralised nature of P2P networks. The core issue in the formation of super peer based

overlay network is the selection of super peer among the participant peers. To solve this problem a number of

solutions have been proposed in the literature. Generally, super peer are selected among the best nodes in the

network, for example those with the most abondant resources, such as bandwidth, CPU cycles or memory. The

next issue is when the peer shall be selected for this extended role either as when peer joins the network, or at

any time during the session or promotion to super peer should be subject to requirements. In order to validate

these approaches of super peer selection, simulation would be an ideal choice, but most existing simulation

approaches cannot cope with unbounded dynamic changes of network topology.

We propose an approach to modelling and simulation of P2P systems based on graph transformations, a visual

rule based formalism that has recently been supported by facilities for stochastic modelling and simulation.

We are considering a P2P VoIP applications such as Skype, we model three alternative solutions to the problem

of peer promotion to super peers and evaluate these through simulation.

1 INTRODUCTION

Today’s P2P network (Milojicic, 2002) contains sev-

eral new and attractive features, which makes them

quite different from classical P2P networks. Al-

though, network may still contain millions of peers.

As a result of this massive number of peers, they are

subject to high degree of churn (Stutzbach and Re-

jaie, 2006), with a number of peers joining and de-

parting from the system respectively. This massive

size of network and geographically diverse location

of peers pose several challenges for developers and

researchers. As immediate affect its impossible to

use either a central authority or ﬁxed communication

topologies. Instead a dynamically changing overlay

topology is used, where control is kept decentralised.

The respective overlay topology is maintained by co-

operation of virtual links between peers, these virtual

connection are created and removed based on the re-

quirements of particular application.

Peers in P2P networks are always in full control

of their local resources and can therefore, any time

impose new policies regarding use of their shared re-

sources in the network (Ji, 2004). A peer may

even suddenly stop its cooperation by behaving self-

ish (Gupta and Somani, 2004). Due to this lack of

global control and unreliability of the P2P architec-

ture, these systems are prone to dependability prob-

lems. Classical P2P applications were lagging the

enforcement of particular overlay topology. The di-

rect result of this approach was adaptation of inef-

ﬁcient scheme such as ﬂooding. However, now re-

searchers and developers have realised the impor-

tance of building and maintaining appropriate topolo-

gies for development of efﬁcient robust P2P Sys-

tems (Zhao, 2003; Rowstron and Druschel, 2001;

Montresor, 2004; Dabek, 2001; Yang and Garcia-

Molina, 2003).

Along with many ﬁle sharing applications (Mon-

tresor, 2004), P2P VoIP is also considering the im-

plementation of structured topologies by distinguish-

ing peer and super peer (Guha et al., 2006). One of

the successful VoIP application developed based on

structure topology is Skype (Skype, 2011; Guha et al.,

2006). The topology is composed of two-level hierar-

chy: Nodes with powerful CPU, more free memory

Khan A. and Heckel R..

MODEL-BASED STOCHASTIC SIMULATION OF SUPER PEER PROMOTION IN P2P VOIP USING GRAPH TRANSFORMATION.

DOI: 10.5220/0003526000320042

In Proceedings of the International Conference on Data Communication Networking and Optical Communication System (DCNET-2011), pages 32-42

ISBN: 978-989-8425-69-0

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

and greater bandwidth take on server-like responsi-

bilities and provide services to a set of client peers.

This approach allows decentralized overlay network

to run more efﬁciently by exploiting heterogeneity

and distributing load to machines that can handle the

burden. It has also overcome the ﬂaws of the client

server model, because of multiple separate points of

failures, thus increasing the health of the P2P overlay

network (Guha et al., 2006; Yang and Garcia-Molina,

2003).

Building and maintaining a super peer based

overlay topology is not simple. Rapid architec-

tural changes in both ordinary and super peers re-

quires robust and efﬁcient protocols, capable of self-

reconﬁguring, in spite of both controlled and selﬁsh

events like joining, leaving or crashing nodes. In case

the P2P is used for VoIP trafﬁc, the network needs

to reconﬁgure fast enough so that Quality of Service

(QoS) is not affected (Khan et al., 2009).

Several questions arise for the design of network

protocols: Which peer should be promoted to super

peer? Can selection of super peer based on the higher

bandwidth is enough? Is promotion at the time of

registering is better from promotion at any time dur-

ing session? How about promotion whenever there

is a need for super peer? The performance of such

a protocol can be measured by answering the ques-

tion: How many peers are connected, how many are

present but yet to be connected, how many super peers

are there, how many clients are happy in the network,

how many VoIP calls have been supported?

Various solutions have been proposed to these

problems, e.g. (Zhao, 2003) suggested the deploy-

ment of super peers directly managed by content ser-

vice providers; (Lo et al., 2005) proposed three dif-

ferent approaches for selection of super peers; (Mon-

tresor, 2004) presented a super peer overlay topology

algorithm and validated his approach using the Psim

simulator; (Oneil et al., 2000; Biondi and Desclaux,

2006; Guha et al., 2006) proposed super peer promo-

tion based on bandwidth, CPU power and time spent

in the network; (Gupta and Somani, 2004) proposes

that an incentive should be given to intermediate

nodes and resource owners; (Heckel, 2005) proposes

to maintain redundant links between peers, (Ren et al.,

2006) propose an autonomous system-aware peer-

relay protocol called ASAP; (Lysne et al., 2005) pro-

poses solutions based on changes in routing strate-

gies; (Yang and Garcia-Molina, 2003) discussed gen-

eral design issues however, their focus is on central-

ized design of such networks.

However, peer dynamics and complexity of P2P

network makes it difﬁcult and expensive to validate

these solutions through testing of real networks. Ge-

ographical distribution of peers, network dynamics

and lack of central control make testing difﬁcult and

costly. The simulation of network reconﬁguration as

well as dynamic role assignment is not easy, as ex-

isting simulators do provide very limited support for

networks with dynamic topology (Heckel, 2005; NS2,

2008; Khan et al., 2010).

We propose to model dynamic role assignment

and associated architectural reconﬁgurations in P2P

VoIP networks by means of graph transformation sys-

tems and use a new approach to the stochastic implan-

tation of such systems to evaluate the performance of

network protocols. We consider the P2P network ar-

chitecture as a graph, in which network nodes are rep-

resented by graph vertices and graph edges represent

network connections. Reconﬁguration in such a net-

work can naturally be modelled by graph transforma-

tion, in a visual and rule-based formalism (Khan et al.,

2009; Heckel, 2005; Khan et al., 2010). Stochastic

simulation techniques for validation have been devel-

oped in (Khan et al., 2009).

In this paper we are going to present a case study

based on the popular VoIP application Skype and dis-

cuss four different variations for promotion of peer to

the role of the super peer.

2 CASE STUDY: SKYPE

NETWORK

Skype is P2P VoIP application developed in 2003 by

the owners of KaZaA. Skype claims that it has cur-

rently more than 200 million users. Real statistics

shows that averagely 25 million users always remain

on-line. It currently contributes more than 8% trafﬁc

to VoIP applications over internet.

Skype architecture of its operation is getting pop-

ularity in P2P research community and Telecom op-

erators, and detailed valuable studies can be seen in

the literature (Baset and Schulzrine, 2006; Biondi

and Desclaux, 2006; Idrees and Khan, 2008). But

due to proprietary protocol, sophisticated nature and

anti reverse engineering techniques (Biondi and De-

sclaux, 2006), many interesting question still remains

unanswered. Since, its ﬁrst release many versions

have been released but the core architecture of the

network still remain the same. Skype network con-

sists of Skype Clients and Super Peers (Baset and

Schulzrine, 2006). The networks nodes are hetero-

geneous in terms of network locality, CPU power,

memory, and most importantly network bandwidth

and type of IP. Skype client with sufﬁcient resources

in terms of bandwidth can promote to the new role of

Super peer, while at the same time, it continues pri-

MODEL-BASED STOCHASTIC SIMULATION OF SUPER PEER PROMOTION IN P2P VOIP USING GRAPH

TRANSFORMATION

mary role of the client for the physical user (Baset

and Schulzrine, 2006; Oneil et al., 2000). Super peers

form an overlay network among themselves whereas

each client has to ﬁrst register with central registra-

tion server and then subsequently select one of the

super peer as their local host or local serving point of

contact (Baset and Schulzrine, 2006). The client will

use super node for searching on-line buddies as well

as for actual trafﬁc routing if client is behind NAT

or ﬁrewall. The registration server is the only server

in the Skype network, responsible for storing user in-

formation including passwords, authenticating users

at login, and provide client with super peer address

for local host connection. All relevant information

regarding on-line users, there current status is stored

in distributed fashion, which does improve the scal-

ability and stability, although these information can

sometime be out of date.

The Skype call cost in terms of the bandwidth

is not clear due to the proprietary nature but analy-

sis in (Baset and Schulzrine, 2006) suggests that call

cost is between 56 Kbps to 16 Kbps whereas (Adami

et al., 2009) states that cost in terms of bandwidth is

25 Kbps when call is active. The client and super peer

also sends each other keep alive messages which con-

sume bandwidth as well. The actual cost is not clear

but (Guha et al., 2006) states that 5 Kbps to 8 Kbps

is the cost of keeping connection with super node or

super node to super node overlay. These keep a live

messages enable both the client and super peer to self-

organise, if the client or super peer has left the net-

work. The super peer based on the local awareness

of bandwidth may accept or reject overlay topology

formation or local host request. Both client and su-

per peer can leave the network either by crashing or

by using cooperative exit procedure provided by the

application GUI.

3 A GRAPH BASED MODEL FOR

SKYPE PROTOCOL

We use graph transformations to model the struc-

tural evolution of the Skype network. As one of the

most basic models for entities and relations, graphs

are a representations of structural models. Formally,

a graph consists of a set of vertices V and a set of

edges E such that each edge e ∈ E has source and

target vertex s(e) and t(e) in V, respectively. More

advanced notions allow for nodes and edges to be at-

tributed with textual, boolean or numeric data (Lara,

2007). Graphs occur at two levels: type level and in-

stance level. A type-level graph is comparable to a

class or ER diagram containing the types of nodes

and edges, declarations of attributes, etc. Instance

graphs represent the states of the system, typed over

the type graph. With graphs as states, transforma-

tion rules provide state changing operations (Heckel,

2005; Khan et al., 2009).

The type graph TG in Fig 1 represents a model of

Skype architecture as described in before. It deﬁnes

the types of registration server (RS), super peer (SN),

Skype client (SC) and their common super type. The

node LK is used to model the link between SC and SN

while OV represents the connection between existing

SNs, to model the overlay topology. The Call and

RouteCall is used to model two different call types.

The edges type ofﬂine is used to show that users is

registered but not currently in the network, online is

used to show when user is successfully authenticated,

overlay-index is used to model the connection be-

tween the SN and RS, route show when call is routed

through the SN, caller is used to show the caller of

the call and callee is used to model the recipient of

the call.

In the model whenever a new SC joins the net-

work it ﬁrst get registered with RS and subsequently

user get connected with RS through ofﬂine edge. A

registered user when joins the network, a client status

SC is assigned and ofﬂine edge is replaced by online.

After this stage the current SC has to select one of the

SN as local host. The SN will be responsible for the

client request such as queering network and if SC is

behind NAT or ﬁrewall, the actual call packets will be

relayed through SN.

In the model SC is promoted to SN based on three

alternate choices. In Fig 2 we have shown these pro-

motion constraints and other mandatory features of

the protocol as feature tree. In the feature tree we

have shown that SC can promote to the role of the

SN based on three choices. First, as soon as it gets

on-line and bandwidth is more than 1.5 Mbps, we

call this approach as static protocol. Second, SC can

promote any time during session in the network, still

bandwidth will be considered, we call this approach

as dynamic protocol. Third, SC can promote to SN

only whenever there is need for a new SN, we call

this as need based protocol.

In order to model VoIP calls trafﬁc, we assume

a codec costing 60 Kbps of bandwidth during active

call. The model supports direct calls in P2P architec-

ture as well as relayed calls. We also randomly update

the bandwidth of the nodes in order to model the be-

haviour of the shared bandwidth and background traf-

ﬁc. In the model if SN leaves the network either by

crashing or cooperative exit, the model is capable to

reconﬁgure the client back to connect to a new SN.

In Figure 2 feature tree shows the mandatory fea-

DCNET 2011 - International Conference on Data Communication Networking

Figure 1: Type graph.

Figure 2: Feature tree.

tures such as go on-line, link SC to SN, load balancing

by simply disconnecting, down grade to client (if SN

is having bandwidth less than the minimum 256 kbps),

VoIP call respectively. In the model an SC can exit by

crashing as well as exit through a cooperative proce-

dure. All these features are kept constant whereas the

promotion strategies are changed in order to check the

performance of different SN promotion strategies.

The objective of modelling these three variations

of promotion of SC to SN is to evaluate different

approaches of promotion against each other. This

will also provide information that which approach has

scaled the network to what number of SNs and SCs.

In addition to that the model will provide information

regarding the performance of each approach based

on the number of connected, unconnected and happy

nodes.

4 SC PROMOTION TO SN AS

GRAPH TRANSFORMATION

A graph transformation rule p : L −→ R consists of

a pair of TG-typed instance graphs L, R such that the

intersection L∩R is well deﬁned. The left-hand side L

represents the pre-conditions of the rule whereas the

right-hand side R describes the post-conditions. Their

intersection represents the elements that are required,

but not destroyed, by the transformation (Heckel,

2005). Graph transformation rules also use negative

application conditions (NACs). A NAC assures that

the rule will only be applied if the pattern speciﬁed

NAC does not match the graph (Heckel, 2005; Khan

et al., 2009). Graph transformation rule also use at-

tributes. The use of attribute enable the rule impose

constraints on the attribute value, which will make

sure that attribute constraint is evaluated in the pre-

condition and attribute value is updated as postcondi-

tion of the rule.

We are now going to introduce a set of transfor-

mation rules based on a simple client promotion to the

extended role of super peer(SN) scenario. Here, due

to limitation of space we are not introducing the rules

for connecting SC to SN, crashing, controlled exits,

whereas the connection rules are already published in

our previous work (Khan et al., 2010). However, in

the simulation all these rules are provided in order to

give results on the complete model.

Rules in Figure 3: Promote a Newly Joining SC to

Extended Role of SN. In this rule a recently on-line

MODEL-BASED STOCHASTIC SIMULATION OF SUPER PEER PROMOTION IN P2P VOIP USING GRAPH

TRANSFORMATION

Figure 3: SC promotion to SN at start of joining.

Figure 4: SC promotion to SN at any time.

Skype client x will be promoted to its extended role

as super peer SN, only if the client x current band-

width is more than 1.5 Mbps and is connected to the

internet without ﬁrewall. After promotion to the new

role, SN client x will still retain the primary role of

the client for the owner user and at the same time will

serve other SCs. Once successfully promoted, client

x informs the server RS about the recent changes to its

role in the network. The static protocol use this rule

to promote SC to SN.

Rules in Figure 4: Promote an SC to Extended

Role of SN at Linked State. In this rule a client

which is already using the network, can be promoted

to the extended role as SN. In this rule a client x,

is having currently sufﬁcient bandwidth and is con-

nected to the internet without ﬁrewall. Further x is

not leaving the network as cooperativeexit procedure.

This client x can be promoted to SN. The attribute exit

informs regarding the intended departure of the client

x. Once selected for promotion, client terminates its

dependency connection with the SN and inform the

server RS regarding the new assignment through edge

overlay − index. The dynamic protocol use this rule

along with rule in Fig 3 to promote SC to SN. This

protocol has the capability to promote at the start as

well as during active session of the client.

Rules in Figure 5: Promote an SC to Extended

Role of SN at Linked State if there is Need for SN.

In this rule an SC which is currently linked with one of

the SN. This linked client can be promoted to the ex-

tended role of SN if the current host SN bandwidth is

less than 1 Mbps. This SN can select client x from de-

pendent clients and promote the same to the extended

role of SN. The client x will be selected based on the

bandwidth attribute value which must be greater than

1.5 Mbps. The need based protocol only use this rule

to promote SC to SN.

Rules in Figure 6(a): Assign Random Value to SN

Bandwidth Attribute. In this rule SN bandwidth

Figure 5: Need based promotion at linked state.

(a) Bandwidth usage and release of SN.

(b) Bandwidth usage and release of SC.

Figure 6: Bandwidth use and release in SC and SN.

attribute will be assigned random value between 500

Kbps and 2 Mbps. The core purpose of this rule is

to change the value of the bandwidth to model other

trafﬁc apart from VoIP in the network. Since, P2P are

highly dynamic most action in the network including

roles of peer depend upon the available bandwidth at

certain time in simulation. So due to this a client may

start network participation with SN but may end up

with a role of SC.

Rules in Figure 6(b): Assign Random Value to SC

Bandwidth Attribute. In this rule SC bandwidth

attribute will be assigned random value between 500

Kbps and 2 Mbps if the SC is connected with internet

through public IP. In the same way this model the traf-

ﬁc that client computer is generating apart from VoIP

application. This is one of the reason that dynamic

protocol use both the rules as in Fig 4 and Fig 5 to

promote at both the stages (Start and linked states).

Rules in Figure 7(a): VoIP Call Request Initiated

by SC with Public IP. In this rule an SC with pub-

lic IP connection with the internet can request for es-

tablishment of VoIP call with other on-line network

participant. Before the call request is generated, SCs

existing calls status is checked by using the NAC con-

ditions. The NACs assure that requesting client SC

must not be involved in already directly established

P2P calls as caller or callee. We have used the node

Call to model the direct P2P call.

Rules in Figure 7(b): VoIP Call Request Initiated

by SC Behind Firewall. In this rule an SC behind

port restricted ﬁrewall can request for establishment

of VoIP call with other on-line network participant,

The on-line participant can either be SN or SC. The

callee of the call can be either connected through pub-

lic IP or behind ﬁrewall. In all cases the VoIP trafﬁc

from this SC will be relayed by the respective host SN

of the requesting SC. The NACs will make sure that

DCNET 2011 - International Conference on Data Communication Networking

(a) SC with Public VoIP call request.

(b) SC behind ﬁrewall VoIP call request.

Figure 7: VoIP call request initiated by SC and SN.

(a) User with Public IP go on-line.

(b) User behind ﬁrewall go on-line.

Figure 8: User go on-line.

requesting SC is not involved in VoIP calls. We have

used the node Routeall to model relayed call through

SN.

Rules in Figure 7(c): VoIP Call Request Initiated

by SN. In this rule an SN initiate request for VoIP

call with other network participant. As stated earlier

SN are clients with extended role as Super peer. An

SN can not only request calls but also relay trafﬁc for

other SCs such as Fig 7(b). The call procedure for SN

is the same as that of in Fig 7(a).

Rules in Figure 8(a): User Go On-line with Public

IP. In this rule a registered user joins the network.

This rules considers that a user is connected to the

internet through public IP. Further, based on static IP

the user is assigned a random bandwidth between 256

Kbps to 2 Mbps. This new user can be considered as

candidate for the extended role of SN if it fulﬁls the

bandwidth requirement.

Rules in Figure 8(b): User Go On-line Behind a

Firewall. In this rule a registered user joins the net-

work. This rules considers that a user is behind a re-

stricted ﬁrewall. Further, the ﬁrewall attribute is set

to true and this user is assigned a random bandwidth

between 128 Kbps to 1 Mbps. This user can not par-

ticipate in the election process of SN as it has ﬁrewall

enabled, which restrict this user to communicate or

coordinate directly in the network. This user will al-

ways be dependent on one of the SN.

5 STOCHASTIC SIMULATION OF

GRAPH TRANSFORMATION

SYSTEM

Stochastic graph transformation (Heckel, 2005) can

be used to model architectural reconﬁguration (Khan

et al., 2009) and non-functional properties such as

performance and reliability. In simple words stochas-

tic graph transformation system (SGTS) is a graph

transformation system(GTS) where each transforma-

tion rule is associated with a positive real number rep-

resenting the rate of the exponentially distributed de-

lay of its application to the model. It is important

to note that graph transformation can not only model

these dynamic networks but it does support a num-

ber of validation and veriﬁcation techniques such as

model checking based on CSL and stochastic simu-

lation based on translation to Markov chains (Heckel

et al., 2006). Model checking seem the right choice

only when abstract properties has to be veriﬁed but

this approach become hard to use when model is

much more complex and dynamic. On the other hand,

Monte-Carlo stochastic simulation is typically based

on the execution of particular processes, which are se-

lected probabilistically by means of a random number

generator (RNG).

Let us consider that a S

= hG , F i is a gener-

alised stochastic graph transformation system when-

ever G is a GTS and F : E

→ (R → [0, 1]) is a

function which associates with every event in G a

general cumulative probability distribution function.

We assume that F(e)(0) = 0 (null delay condition)

(Khan et al., 2009). Moreover, the probability dis-

tribution is dependent on the event (rulename and

match) rather than just the rule. The concept of the

SGTS is explained (Heckel et al., 2006) in detail. Our

interest in stochastic graph transformation systems is

closely associated with their simulation, where the

stochastic aspect is useful in order to resolve the non-

deterministic character of ordinary GTSs.

We simulate our model using GraSS (for Graph-

based Stochastic Simulation), a tool introduced in

(Torrini et al., 2010) and used for our previous work

MODEL-BASED STOCHASTIC SIMULATION OF SUPER PEER PROMOTION IN P2P VOIP USING GRAPH

TRANSFORMATION

(Khan et al., 2010). The tool has been developed

in Java-Eclipse, as plugin of a graph transformation

engine called VIATRA. VIATRA (Bergmann et al.,

2008) relies on a RETE-style implementation of in-

cremental pattern-matching, in which precomputed

matching information is stored and updated as trans-

formation proceeds. The architecture of the tool is

shown in Fig 9. Essentially, the stochastic engine re-

ceives the set of enabled rule matches (i.e.the active

events) from the transformation engine, turns them

into timed events, by assigning to each of them an

expected time value, randomly determined on the ba-

sis of the probability distribution which is associated

with the event type, and sends the events that has been

scheduled ﬁrst back to the transformation engine for

execution.

In GraSS a GTS is represented as a VIATRA

model, consisting of the model space with the current

graph and the transformation rules. Moreover, GraSS

takes as input an XML ﬁle with the deﬁnitions of the

distributions associated with transformation rules and

respective rates. In order to collect statistics the rules

with empty post-conditions that are used as probes

as can be seen in the architecture Fig 9. Each probe

rule returns the number of its matches in the current

graph for each state of the transformation system. We

used a number of probe rules for collection of simula-

tion results in this paper for the purpose of reader un-

derstanding we are presenting one probe rule in both

graphical representation in Fig 10 as well as VIATRA

code translation shown below:

gtrule SC_linked_SN()=

{

precondition pattern lhs(SC,SN,LK)=

{

SN(SN);

SC(SC);

LK(LK);

find LK_LinkTo(LK,SC);

find LK_OutTo(LK,SN);

}

action

{

println("SC linked with SN");

}

This probe is used to ﬁnd average number of

SCs that are linked with SNs. Additional parameters

needed for a simulation run are provided to GraSS as

part of the VIATRA model (see (Torrini et al., 2010)).

The textual output of a simulation experimentconsists

of SSJ TallyStore class reports (L’Ecuyer et al., 2002).

In this experiments we are going to compare three

different protocols for SC promotion to SN. We have

used time based simulation, in order to produce com-

parative results. We have taken simulation unite as

24 hour for these experiments. We use exponential

distribution as will as normal distribution. Although

due to limitation of space it is not possible to present

complete set of rules along with respective probabil-

ity distribution and necessary justiﬁcation. We have

used normal distribution for all those rules for which

implementation boundaries are known. Based on this

we have used normal distribution for rule that termi-

nates VoIP calls by keeping in mind that experiments

in (Guha et al., 2006) conﬁrms that minimum call du-

ration observed was 2 minutes(m) and 50 seconds(s)

and maximum observed duration was 3 hour(h) and

26 m whereas the average as per there experiments

was 12m and 53s. Further, we have used exponential

distribution for rules presented in this paper at Fig 8.

As we are not sure that when a user will go on-line

so the rules that makes user to go on-line have been

assigned exponential distribution. Similarly, the pro-

motion rules use same exponential distribution.

We performed two different experiments in which

we run several simulations of each of the three pro-

tocols based on 24 hour simulation time. In the ﬁrst

experiment we varied the rate of the rule that make

client on-line by{ 3,4,5,6,7}. In this experiment a sin-

gle rule is used which makes user to go on-line. This

rule also randomly set the ﬁrewall to true and false.

The aim is to simulate such behaviour that model does

not have any control on the population behind ﬁre-

wall and with static IPs. Due to limitation of space

this rule is not presented in the paper. In the second

experiment we have ﬁxed the rate of the rule in Fig

8(a) at 5 and we varied the rate of rule in Fig 8(a) by{

3,4,5,6,7}. The aim behind this is to reduce the num-

ber of candidate for SNs and increase the number of

SCs behind ﬁrewall. The rates for these rules either in

experiment 1 or 2 are selected based on the assump-

tion that if Skype user gets on-line every 8 hour over

24h period then rate based on this principal would be

3, and so on. The aim behind these varying rates is to

produce same number of average as that of real Skype

network (SkypeStatistics, 2011) in the 24h period in

order to conﬁrm the conﬁdence of the model.

In order to comment on the performance of these

three protocols, we have used several probes rules

such as to ﬁnd numbers of SCs, SNs, linked SCs, and

number of clients that are happy with existing SN. In

our experiments an SC is happy with current SN if

its current host is having more than 1 Mbps available

bandwidth.

DCNET 2011 - International Conference on Data Communication Networking

Figure 9: Graph based stochastic simulation (GraSS).

Figure 10: Probe rule SC connected with SN graphical view.

6 SIMULATION RESULTS

In the ﬁrst experiment we compared three approaches

of client promotion to extended role of SN. Each ap-

proach/protocol is represented by a model and set of

transformation rules. All three models were tested

through 5 variations of rate x for the clients join-

ing the network. The rates assigned were ranging {

3,4,5,6,7}. For each variation we performed 9 runs

with a time unit of 4.8 hour. The results are presented

as graphs in Fig 11. In this experiment the number

of SCs with static IPs and behind ﬁrewall randomly

joins the network and their ratio is not known.

The graph in Fig 11(a) presents the percentage of

the happy peers in the network. As the graph shows

that dynamic VoIP protocol for super peer selection

approach is performing better as compared to other

two at the joining rates 3 and 4. The graph in Fig 11(a)

further shows that at joining rate 5, the number of

happy peers are almost the same but at rate 6 and 7 we

observe that, as the number of clients in the network

increases, the need based approach tends to produce

good results as compared to other two approaches.

The graph in the Fig 11(b) presents the average

number of linked clients. From graph we see that

dynamic protocol has resulted in well connected net-

work. Although, the other two protocol also managed

to link a good number of SCs to SNs. We further see

that in terms of SC connection to SN the other two

approaches are almost performing at the same level.

The graph 11(d) shows the average number of SNs

promoted in this course of simulation. The graph

results shows that there is not a big difference be-

tween the SNs promoted by all the three protocols.

Although, need based approach promoted less num-

ber of SNs but in terms of the happy peers the results

are not much different from other two protocols ap-

proach.

The third graph in the Fig 11(c) further clarify

that that all the protocol managed to result in network

nodes between 250 and 500. Although need based

protocol has slightly less number of clients in the net-

work but the difference in comparison with other two

protocol is not much. During the simulation the total

number of clients were ﬁxed at 1000.

Th results of ﬁrst experiment shows that at joining

rate 5, all the three approaches managed to produce

results which are close enough. In order to further

conﬁrm these results we split the single rule of joining

into two as presented in Fig 8. Now we have ﬁxed

that rate of the rule Fig 8(a), which makes clients on-

line and clients are enjoying static internet connection

without enabled ﬁrewall. The aim is to ﬁx the number

of candidate for SN and we varied the rates for the

rule Fig 8(b) by { 3,4,5,6,7}. The aim is to increase

the number of users behind ﬁrewall. The results of

this experiment are presented as graphs in the Fig 12.

The graph in the Fig12(a) conﬁrms that need

based protocol is performing much better as com-

pared to other two approaches when the number SCs

behind ﬁrewall increases in the model. Although we

do observe that in the start the dynamic approach is

performing better as compared to other but at joining

rate 5 where both rules are ruining at the same rate,

the results are changed and need based continues to

produce better results as the number of SCs behind

ﬁrewall increase. The second graph in Fig12(b) the

average number of SCs behind ﬁrewall in each rates,

which are almost close to each other in all the three

approaches.

7 VERIFICATION AND

VALIDATION OF SIMULATION

MODEL

Veriﬁcation and validation of the simulation models

are the core entities in the modelling and simulation

study. There are various methods used in the liter-

ature for this purpose (Sargent, 1996; Whitner and

Balci, 1989). In this study we have used static and

dynamic veriﬁcation techniques in order to make sure

that model has rightly been converted to VIATRA

model and the associated transformationrules are also

rightly converted. The static technique has ensured

MODEL-BASED STOCHASTIC SIMULATION OF SUPER PEER PROMOTION IN P2P VOIP USING GRAPH

TRANSFORMATION

(a) Percentage of happy SCs.

(b) Average numbers of SCs linked to SNs.

(d) Total average number of SNs.

Figure 11: Simulation results ﬁrst experiment.

that model and rules are error free and right syntax

has been followed. The dynamic veriﬁcation tech-

nique has ensured that each rule does the task that it

was suppose to do.

Similarly for the purpose of model validation we

have used face validation, event validation as well

as compared the model with real system (Sargent,

1996; Whitner and Balci, 1989). Fore comparison

with real system we have used the study in (Guha

et al., 2006) and Skype statistics from (SkypeStatis-

(a) Percentage of happy SCs.

(b) Average numbers of SCs behind ﬁrewal.

Figure 12: Simulation results second experiment.

tics, 2011; SkypeJournal, 2010). The author analysis

in (Guha et al., 2006) is based on real system study,

their results shows that over a period 24 hour,the aver-

age number of clients that join the network varies by

over 40% of the active registered accounts, whereas

the average number of super node in this period is

below 24% of the active population. Similarity, the

author in (SkypeJournal, 2010) states that in Decem-

ber, 2010 there were 1.4 million super peer/nodes and

25 million user were on-line, when Skype network

crashed due to non availability of super peers. This

ﬁgure conﬁrms that almost 6% of the on-line user

were super peers and still Skype network crashed.

This further conﬁrm that Skype super peer population

must be over 6% of the on-line users, in order to make

networks stable. Based on these results we have ex-

amined our model simulation results obtained over a

period of 24 hour simulation. The simulation results

conﬁrms that super node population in our model is

less than 24% which conﬁrms the results of the (Guha

et al., 2006) and are over 6% which further conﬁrms

the statement of the author in (SkypeJournal, 2010).

Our model further conﬁrm the overall average num-

ber of population with real statistic of (SkypeStatis-

tics, 2011; Guha et al., 2006). Once we have obtained

these results we have ﬁxed the rates of rules and var-

ied the rates of the rules where we have to make sen-

sitivity analysis.

DCNET 2011 - International Conference on Data Communication Networking

8 CONCLUSIONS

In this paper we have outlined our simulation ap-

proach based on stochastic graph transformation. We

used it to model and simulate some aspects of P2P

VoIP network protocols, and we have performed our

experiments with the GraSS/VIATRA tool (Torrini

et al., 2010). We have compared three client promo-

tion to exteded role protocols. The dynamic proto-

col does not seem to be performing better as com-

pared to the need based and static protocols in terms

of happy peers, especially when the number of clients

in the network increases over 400. The results fur-

ther conﬁrmed that increased in super peer does not

mean that network may also result in good number of

happy clients. We further observed that need based

protocol is most suited when there are greater number

of clients, as super peer promotion costs in terms of

bandwidth use.

As future work, we are planning to extend the

model and include spatial information regarding no-

tions of jitter, packet loss and echo, along the lines

of (Khan et al., 2009), and to compare a number of

different design solutions to problems such as rout-

ing, load balancing, selﬁsh exit, and cooperative exit

from the network, in order to investigate their trade-

offs and beneﬁts.

ACKNOWLEDGEMENTS

This research is supported by Universityof Malakand,

Pakistan through faculty development programme of

HEC, Govt. of Pakistan.

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