=Paper=
{{Paper
|id=Vol-1256/paper8
|storemode=property
|title=A Derived Queueing Network Model for Structured P2P Architectures
|pdfUrl=https://ceur-ws.org/Vol-1256/paper8.pdf
|volume=Vol-1256
|dblpUrl=https://dblp.org/rec/conf/vecos/MordjiAA14
}}
==A Derived Queueing Network Model for Structured P2P Architectures==
https://ceur-ws.org/Vol-1256/paper8.pdf
76
Derivation of a Queuing Network Model for
Structured P2P Architectures
Zouweyna MORDJI Mourad AMAD Djamil AÏSSANI
LaMOS research unit LaMOS research unit LaMOS research unit
Faculty of Exact Sciences Faculty of Exact Sciences Faculty of Exact Sciences
University of Béjaia University of Béjaia University of Béjaia
06000 Béjaia, Algeria 06000 Béjaia, Algeria 06000 Béjaia, Algeria
mordji.zouweyna@gmail.com amad.mourad@gmail.com Djamil.AISSANI@gmail.com
Peer to peer (P2P) networks have using commonly used for tasks such as file sharing or file distribution, and
for building distributed applications in large scale network. Their performance measures are generally based
on simulation methods software such as NS-2, P2PSim, OpenNet, etc. Hence, the absence of a validation of
the simulation model is a critical issue. In this paper, we propose a new analytical model derived from (8), to
evaluate the performance of HPM protocol (hierarchical Peer-to-Peer model). Performance is done principally
in terms of total download time of requested resources in the P2P network, and then we analyze the impact
of various parameters associated with the heterogeneity of nodes.
P2P, Performance evaluation, Analytical model, HPM, Queuing model.
1. INTRODUCTION (8), (9), (2). In this paper, we follow mostly the
approaches put forward in (8).
The P2P paradigm has emerged as a solution to The goal of this paper is to propose an analytical
some limitations of the classical methods of resource model for evaluating the performance of the HPM (hi-
sharing based on the paradigm Client / Server. It is erarchical Peer-to-Peer model) (13). Our proposed
a distributed system without or with minimal central model is different from those explored in (8), in
authority and with varying computational power at their work, the structured P2P systems have not
each machine. Its applications are varied, we cite as been addressed. Our work is then to complete the
an example: the multicast application, parallel com- analytical model proposed in (8).
puting, file sharing, IP telephony, instant messaging, We interest about structured P2P architecture, be-
search engines, etc. This type of network is generally cause it is more efficient in terms of lookup and
characterized by a good scalability (scaling) and download resources, and more complicated to im-
a very high dynamic (churn rate), for more details plement. For this, the analytical model is slightly
about this topic see (1). more interesting to take into account the system
P2P networks have seen an unprecedented develop- characteristics and evaluate the performance of the
ment that was accompanied by a significant increase corresponding architecture in a very short time, and
in their complexity. So, we focus in this paper on give a good insight into the operation of the systems
analytical models, because of the interest in their under study at low cost, compared to other perfor-
high speed resolution. Indeed, when considering mance evaluation techniques of P2P networks like
making a change to the system, decisions will lead measurement and simulation approaches. Analytical
to very high cost, and it is very useful to have an- models are least expensive and give the modeler
alytical solution with their much reduced computing deep insight into the main characteristics of the
time. Analytical and mathematical frameworks let us system.
to model and study the performance of the P2P In this work, we want, exactly, to answer the ques-
networks, and several models have been proposed tion: using the HPM, how long does it take a re-
in order to investigate the dynamics of this kind quested resource to lookup and download? To an-
of systems, many researches are focused on the swer this question, we use a queuing model with
Markov chain based modeling , (7), (3),(4), (10), and structured P2P system, we consider two types of
recently the researchers exploit the queuing model nodes, the relay and the end peer nodes as de-
for performance evaluation of the of P2P networks scribed in HPM, we use also a single class open
77
queuing network to evaluates the delays in a relay
nodes, we model each relay node as G/G/1 queue
(13) and the end peers as M/G/1/K processor shar-
ing queues.
The rest of this paper is organized as follows: next
section gives a background and related work on
Peer to Peer networks and existing performances
evaluation methods, we describe and analysis the
proposed models existing in the literature. Section
3 describes our proposed model. In section 4, we
validate our model; finally, we conclude and give Figure 1: Classification of P2P systems
some perspectives.
Centralized Systems (CSy): consists of a single
2. BACKGROUND AND RELATED WORK server that is responsible to relate directly all
connected peers and to identify the files offered by
In this section we give a brief description of
different clients. The advantage of this technique lies
P2P network and different classes of associated
in the centralized indexing all directories and titles
mathematical models.
of shared files by the subscribers in the network.
2.1. Background Clients send queries to the server, and it returns a
list of peers currently connected to the service and
P2P Systems offer an important opportunity for a who’s shared the desired files. The file transfer will
large number (hundreds of thousands) of nodes be done between final users and not by the server.
to cooperate in order to share resources via a Under these conditions and at any time, files are
widely distributed network. Nodes of the network, found stored on the central server. Such centralized
are an equal participant, and there are no nodes approach does not scale well and have a single
with special facilitating or administrative roles. Since point of failure, (e.g., Napster ).
the service is distributed to all participating nodes,
the system is expected to scale well even when Decentralized Unstructured Systems (DUSy): it
the network is very large. Avoiding bottlenecks and is called also the pure P2P systems in which all
likely with good fault tolerance, the P2P paradigm nodes play equivalent roles, there are no servers
is suitable for large-scale distributed environments or nodes privileged, each node has high degree
where nodes (called also peers) can share their of autonomy. Nodes are organized arbitrarily using
resources (eg. computing power, storage capacity, flooding (broadcast or random walks) for the content
bandwidth) as an autonomous and decentralized. discovery. To find a resource, a request will be sent
Due to its advantages, several areas have already from a peer to another until it reaches the client that
taken advantage of this paradigm (eg. file sharing, has the desired object. To avoid flooding the network
sharing computing capacity and exchange instant for too long, the system associates each request a
messages). A peer can play the role of client timer TTL ”Time To Live”, the value assigned to the
when it consuming resources, and the role of TTL is usually 7 (as in Http). When it reaches zero,
server when it offered resources, router when it the query is not returned. The major disadvantage
spreads requests received from other nodes in the of this mechanism comes from the expiration of TTL
system, and host data source when sharing their before the course of the entire network, which can
data with other peers. There are many different lead to failure of research although the desired file
P2P systems, each one with various advantages is available on the P2P network, and usually, these
and disadvantages. They differ both in their object networks do not scale well, because of the high
query mechanism and in their logical topology, we amount of signaling traffic. On the other hand, they
therefore distinguish three families of P2P systems: present a very high level of anonymity. The most
centralized systems,decentralized (structured and known examples of these networks are Gnutella and
unstructured) systems, and hybrid systems. FreeNet .
Decentralized Structured Systems (DSSy): the
emergence of structured P2P systems is due to the
problem of large number of messages exchanged
in unstructured P2P systems. Nodes should be
structured in a precise geometrical form, and in
general, they consist in some variant of a Distributed
Hash Table (DHT) technology. These networks are
78
constructed in a structured overlay where each node models, fluid flow models, and queuing network
maintains a specific set of contents (or a set of models. In most cases, these models are used to
content location indexes), this information is often describe the performance of the whole system and
used to guide the routing of the requests / messages stochastic characteristics of a peer, they are clearly
in the system. Therefore, the content searches are able to reflect the effect of different parameters on
deterministic and efficient. As examples of their P2P systems performance, they permit efficient
systems, we can cote: Chord, HPM (11). and detailed exploration of the parameter space to
evaluate the effect of not just only single parameter,
Hybrid Systems (HSy): hybrid P2P network is but also the combined effect of variation of several
more complex to implement, as it combines both parameters. However, many of these models are
centralized and distributed network. A network of this based on unrealistic assumption like peers having
type is based on a set of servers managing a group global information about the state of all peers,
of users according to the centralized architecture. simplifying assumption on the underlying network
Each server is then connected to other servers topology, and on the arrivals and departures of
according to the distributed architecture. peers.
In this way, if a user searched a file that is not
indexed by the server to which it is attached, it 2.2. Related Work
then forwards the request to another server. This
architecture can benefit from better bandwidth while In the following, we present the different analytical
reducing the query traffic. models used to evaluate the performance of P2P
In this paper, we are interested in the structured networks:
P2P architecture in general and particularly HPM
(11). HPM is composed of a set of hierarchical rings,
Fluid Flow Model: An homogenous branching
which consist of the nodes that are neighboring
process is used to study the service capacity
in terms of physically proximity, without distinction
of BitTorrent-like P2P file sharing network in the
between nodes in different levels, and it is based on
transient regime and a simple Markovian Model is
a hash function and cryptographic for the identifiers
presented in (3) to study the steady-state properties.
of resources, the IP address and port number for
They found that the capacity of such systems
the identifiers of nodes. HPM routing objectives
grows exponentially in transient and stabilizes
are: provides the discovery/localization service,
at steady state. Various techniques are studied
based on a complete decentralized architecture, by
that might help to improve P2P performance.
determining with efficiency the node responsible for
Multi-part combined with parallel uploading when
storing the requested key’s value.
properly optimized will generally improve system
One of the main characteristics of HPM is the routing
performance, particularly when peers exit in the
optimization at IP level, as it takes into consideration
system at a high rate. The above work is extended
the physical proximity while minimizing the number
in (4) where simple deterministic Fluid Model is
of hops for lookup process (cost lookup). The
derived from Markovian model proposed in (3),
authors evaluated the performance of HPM with
in order to study peer number temporal evolution
simulation, the metric they are taken: cost lookup,
and average downloading time in BitTorrent-like file
size of data structure, number of rings at each level
sharing systems. Furthermore, other features of
and the number of rings and level for HPM with IPv6
BitTorrent networks such as downloading efficiency
and IPv4 address format. However, in our work, we
and incentives are discussed.
evaluate the system with analytical model in term
In (6), the authors develop an analytical model
of total download time of requested resource, and
allowing to study the effect of network characteristics
capture the impact of nodes level characteristics on
on P2P file sharing system performance. Particularly,
the performance of HPM.
they have focused on access link capacity and
Mathematical models can be used to predict system
heterogeneity. In (5), a simple fluid model, (an
behavior. Among both techniques: simulation and
extension of (4)) is proposed, the authors analyze
analytic modeling that can be used at the design
the effect of bandwidth heterogeneity on file transfer
stage, this one is much less expensive. Also,
dynamics and content diffusion process in detail.
with the availability of very powerful and effective
They compare the performance of heterogeneous
general purpose modeling tools, analytic models
networks and the equivalent homogeneous networks
are becoming increasingly more cost effective than
under different conditions of equivalence. Their
simulation. Many researches are focused on this
results show that heterogeneity bandwidth can have
modeling method for evaluating the performance of
a positive effect on content propagation.
P2P systems; the most significant classification of
the modeling techniques we found in the literature,
Markov Chain Model: Birth and Death Markov
they are classified into four models: Markov chain
model based structured peer-to-peer networks are
79
studied on (7). The result shows that the structured 3. PROPOSITION
peer-to-peer network is very suitable for networks
with low dynamicity. The authors in (? ) study the In this section we develop our proposition model,
dynamic and robustness properties of large-scale which consists of modeling the HPM structured
peer-to-peer systems. They propose an analytical P2P system, and evaluate its performances with
model of the local behavior of clusters, based on an analytical method. This work is an extension
Markov chains to evaluate the impact of malicious of (8). The authors of (8) did not evaluate withe
behaviors on the correctness of the system, and their analytical models the performance of structured
analytically evaluation of the performance of the P2P systems, so we want to complement their work
global system, allowing to characterize the global and study case not treated. For this, we use a
behavior of the system with respect to its dynamics queuing model to model and evaluate the HPM. As
and to the presence of malicious nodes. The focus described in HPM architecture, two types of nodes
of these studies is primarily on the evolutionary is considered, the relay and the end peer, the relay
dynamic of the system. These studies also do not node represents a gateway between rings. We use
account for queuing effects and heterogeneities in a single class open queuing network to model and
hosts and the network. evaluate the delays in relay nodes, we model each
relay node as a GI/G/1 queue like in (13) and the
Queuing Network Model: the famous model end peers as M/G/1/K processor sharing queues.
of P2P file sharing systems is presented in (2), in
which a multiple class Closed Queuing Model was 3.1. Functional Principal
proposed to capture distinguishing characteristics
HPM is organized as a set of hierarchical rings
of P2P file sharing systems, This model is applied
composed of nodes, we interested in two types of
in three different types of architecture (Centralized
nodes: relays and peers nodes. Each relay acts as
Indexing: CIA, Distributed Indexing with Flooded
a gateway to one or more rings, and peers are
queries : DIF, and Distributed Indexing with Hashing
the nodes residing in the various ring. We take
directed queries: DIHA), and it is used for analyzing
as example the scenario below: three relays (R1,
important aspects regarding performance like
R2 and R3) and four rings as shown in figure 2.
system scaling, freeloaders, file popularity and
When a peer P2 in ring 2 searches a file that is
availability. This model does not capture the
on peer P9 in ring4, the request (packet) should be
significance of the physical underlying topology of
transferred through the R1 and R2 relays to get the
the considered P2P network. In (8), an analytic
file that on P9, (the principal detailed of the lookup
framework to evaluate the performance of peer to
and download of resources in HPM is described
peer networks is proposed. The authors used as a
in (11)), so, how long does it take to lookup and
metric: a time to download or replicate an arbitrary
download a requested resource?, : to answer this
file. Their proposed model captures the impact of
question, we must first get query search time, the
various networks and peer level characteristics on
transmission time of the file being downloaded, and
the performance of P2P network, and they propose a
queuing delay at the intermediate relay, the sum of
queuing model which evaluates the delay of routers
the three quantities provides us the total resource
using a single class open queuing network and
transfer time. For this, in next section, we studied
the peers as M/G/1/K processor sharing queues.
and analyzed each point separately, and we use a
An important abstraction unaddressed in is the
queuing model to model relays and the peers and
availability, and dynamism of nodes in term or churn
evaluate the total delay to download a requested
rate (disconnection/connection) for P2P network,
resource in the HPM architecture.
which can influence on total network latency. In (9),
the same authors evaluate the file transfer delay
at the peers, and contributed more compared to
their previous work in (8), the case of online-offline
transition of peers and gives the total peer latency.
In this work, we are interested to apply the proposed
analytical model (8) in order to give performance
evaluation of structured P2P systems, a case
study concerns HPM protocol (11). In table 1, we
summarized the work discussed in this section, we
gave the focus of analyses and result, and the weak
point of each work.
Figure 2: example of lookup and download in HPM
80
We use the notations bellow: Determine two parameters for each relay j:
(i) the arrival rate λj can be obtained from the traffic
• n : number of internal relays in the network. for rate equations:
each j, j = 1,...,n
• λ0j : expected external arrival rate at relay j ∑
n
λ0j = [1/E(A0j )] λj = λ0j + λij , f orj = 1, ..n, (1)
i=1
• Ca00j : squared coefficient of variation (scv) or
variability of external interarrival time at relay j: where λij = pij λi , is the expected arrival rate at
Ca20j = [V ar(A0j )]/[E(A0j )2 ] station j from station i.
We also get :
• µj : expected service rate at relay j: µj =
1/E(Sj )
ρj = λj /µj , 0 ≤ ρj ≤ 1, (2)
• 0
CS0j : scv or variability of service time at relay
j, CS00j = [V arSj ]/[E(Sj )2 ] (ii)the squared coefficient of variation (scv) for the
arrival process or variability of interarrival time.
• pij : for each pair (i,j), probability of a packet The expected (external) departure rate to station 0
going to relay j after completing service at relay from station j is given by :
i
∑
n
3.2. Analytical Model of HPM λ0j = λj + (1 − pij ). (3)
i=1
We focus on the network queuing delays and the
delays at the end peers, using a queuing model. We Throughput or total external rate of traffic into the
break up the system into two components: the relay relays :
nodes, modeled with single class open network,
GI/G/1 OQNS, and the end peers modeled with ∑
n ∑
n
M/G/1/K Processor Shared. λ0 = λ0j or λj0 (4)
j=1 j=1
.
3.2.1. Relay Network Model The expected number of visits
In our proposition, we use a decomposition method
(13),(14), that consists of decomposing a network vj = E(Kj ) = λj /λ0 . (5)
relay nodes into smaller sub-networks and then
analyzing each sub-network separately which it The s.c.v. of arrival time can be approximated by
consist of individual queues. In this approach, a Traffic variability equation (8):
network is approximated as a set of individual
isolated GI/G/1 queues. Performance metrics at ∑
n
λij
each queue are computed using approximation
2
Caj = wj 2
Cai + 1 − wj (6)
i=0
λj
formulas for the GI/G/1 queue.
We model each relay nodes by a GI/G/1 to allow , where
for arbitrary arrival and service time distribution.
1
Traffic to a network relay can be rather irregular and wj = ,
does not necessarily follow a Poissonien distribution 1 + 4(1 − ρj )2 (xj − 1)
(15),(16), and may vary from network to another. and
Given this, we model our network with generalized 1
inter-arrival (GI) process. xj = ∑n λij 2
.
i=0 ( λj )
To find the relay network delay, we should pass
through three steps:
Step 1. Analysis of interaction between relays of the Step 2. Evaluation of performance measures at
networks, each relay
Step 2. Evaluation of performance measures at each The expected number of packets in the j th relay,
relay, including one in service, is given by using Little’s law:
Step 3. Evaluation of performance measures for the
whole network. E[NCj ] = ρj + λj E[WQj ] (7)
The expected waiting time at the jth relay is given by
Step 1. Analysis of interaction between relays of :
the networks
81
E[Np ] represent the expected number of resource
ρj (Ca2j + CS2j )g(ρj , Ca2j , CS2j ) transfers in progress at the end peer at any given
E(wj ) = (8)
2µj (1 − ρj ) time, it is given by:
∞
∑
where g(ρj , Ca2j , CS2j ) = E[Np ] = ipi (13)
{ } i=1
−2(1+ρj )(1−Ca2 ) 2
j 2
exp 3ρj (Ca2 −CSj )2 , Caj > 1),
3.2.3. Query Search Time
j
2
1, Caj ≥1 The expression of query search time is the time
taken for the entire search process to terminate; it
differs from one architecture to another, depending
Step 3. Evaluation of performance measures for on the research technique used. In this work, we
the whole network consider a structured architecture to evaluate this
The total number of packets in the network is: parameter, which is the HPM, so, the neighbor
∑
n relationship between peers and data locations is
NC = NCi . (9) strictly defined. Searching in such systems is
i=1 therefore determined by the particular network
The relay delay per packet: architecture. The search technique employed to
lookup the requesting resource in this architecture
NC is defined as follow:
E[TN r ] = (10)
λ0 Each ring k at level i, used the ith part of data key
for the lookup process, when a peer in ring k if the
3.2.2 The End Peers requestor node belongs to, the request succeeds on
The HPM architecture is composed of peers and this ring k, if the resource does not exist on the active
relays, each relay is attached to a number of rings; covered ring, the search is done on ring level i + 1, or
in turn harbor the end peer. In the previous section, i−1, in a deterministic
∑m manner the cost of the search
we provided a queuing delay at the intermediate process is O( i=1 log2 (ni )), where, ni is the number
relay, and in this subsection, we give and develop of nodes on the covered ring at level i on which the
a queuing model for the end peer and provide request succeeded.
expression of the expected time takes to service a The query process terminates when the last of
requesting resource. We model each end peer as the responses finds it’s way back to the source.
M/G/1/m Processor sharing. The choice of this last is The expected time elapsed between the query
motivated by the fact that, the service time depends generation and termination is thus:
on the size of the resource being downloaded and
resource size distribution is typically heavy-tailed, ∑
N
E[TQS ] = [2C ∗ d (E[WQi ] + τi )]/NR , (14)
so the service time cannot be modeled as an
i
exponential process. For this, we are motivated to
choice an arbitrary distributions for the time services ∑N
where [ i (E[WQi ] + τi )]/NR represent the average
and taking generalized model for resource size, and queuing delay at a relay, and [WQi ] is given
the arrival process follows the Poisson process with previously in Eq.(14)
rate λdi , since the SCV of the arrival process at the The factor of 2 comes in since the query response
end peers equals 1, the demonstration of this result traces the same forward path back to the query
is given in (8). originator.
State probabilities pk are given by: C is the cost of the lookup in HPM architecture, and
is given by:
k m
ρ (1−ρ) ρ (1−ρ)
pk = 1−ρm +1 , Pl = 1−ρm+1 , ρ = λdi X̂, (11) ∑m
C = O( log2 (ni ),
i=1
for k = 0, 1, ..., m. where Pl is the loss probability, d give the approximate distance for random graph,
and X̂ is the average service time per request. it represent the shortest path between two random
Using Little’s Law, the expected service time that a chosen nodes on the relay graph:
user encounters can be expressed as:
ln(NR − 1)(ẑ2 − ẑ1 ) − ln(ẑ12 )
d= ,
E[Np ] = λp (1 − Pl )E[wp ], (ln(ẑ2 /ẑ1 ))
E[Np ]
E[wp ] = (12) where ẑi is the average number of i hop neighbors
λp (1 − Pl )
and NR is the total number of nodes in the relay
82
graph: The final expression for the overall waiting time,
E[T ], gives :
∑
NR ∑
NR
ẑ1 = [ Aij ]/NR , ẑ2 = [ IÂ (i, j)]/NR
i,j=1 i,j=1,i̸=j E[T ] = E[TD ] + E[TQS ] (18)
A is the relay adjacency matrix, Â = A2 and IA (i, j)
defined as: 4. CONCLUSION AND FUTURE WORK
{
1, if Âij > 0, In this paper, we have presented the performance
IÂ (i, j) =
0, otherwise evaluation models for P2P systems, which of these
P2P overlay networks is best suited depends on
3.2.4. Expected Download Time the application and its required functionalities and
We arrived at the expression that gives the total performance metrics (e.g. scalability, network routing
download time of resource, which is the time elapsed performance, location service, file sharing, content
from when the query was generated until the entire distribution, and so on).
resource is downloaded, with O(i) copies of the
resource in the network, which is generated by the
We have summarized various recent works on
Zipf’s Law :
performance modeling of such systems that have
O(i) = Von /iθ Hθ (V ), been proposed in the literature, offering an insightful
and useful overview of system properties, focus of
analyses and results of each work studying.
where Hθ (V ), is the harmonic number of order θ of
V and defined as:
A novel analytical model derived from work in (8)
∑
V
is proposed in this paper, it consist of evaluating
Hθ (V ) = 1/iθ . the performance of structured P2P network, we
i=1
have take as an example the HPM architecture and
as performance metrics the total download time of
The given formula in Section 3.2.1. gives us the total requested resources.
time it takes a packet takes to get the customer
E[TN R ], so the download time is determined by the
time spent by the last packet sent by the slower peer As future work, we envision to take into account the
to reach the destination. behavior of nodes and we will study the online-offline
The time when the last packet reaches the edge transition, which may influence the performance of
of the network is when the slower peer is done the system, and especially on the download time of
transmitting it’s allocated resource part i.e. after a resource.
E[TW P ] seconds. The packet, then spends a further
E[TN R ] in the network.
The expected service time for data transfer at the
slower peer is:
B/O(i)
E[TW P ] = (15)
C/E[NW P ]
B is the total file size,
O(i) number of copies of the resource in the network
E[NW P ] is the expected number of files serving at
any point in time
∞ ∑
∑ j
E[NW P ] = [ i ∗ p(i)]P (m = j) (16)
j=0 i=0
Thus, the total download time, E[TD ], is given by:
E[TD ] = E[TW P ] + E[TNR ] (17)
83
Ref. Analytical Architecture Focus of Analyses and Re- Weak points
Method sults
(2) CQMo CIA,DIFA,DIHA Generality, flexibility of mod- Not capture the effect of the
eling,analyze the effect of differences in the file size of
freeloaders, files and user be- different request on the sys
havior. performance, access rate and
varying load on different peer
not modeled, ignore the effect
of the network topology.
(3) MMo,Bpr DUSy (BitTor- Study service capacity and Performance of individual user
rent) fairness. P2P system achieves not degrades significantly, the
favorable scaling in terms of average delays scale well in
average download delay with the offered load Not account
increasing load. for queuing effects and hetero-
geneities in the network.
(4) FMo DUSy Study the scalability and in- Not account for queuing ef-
HFflow centive mechanism, The sys-
(BitTorrent- fects in the network, and
like) tem scales well with the num- heterogeneities in hosts and
ber of peers, the incentive the network. The assumption
mechanisms are efficient, op- about global knowledge of all
timistic unlocking may encour- peers for peer selection
age free-riders.
(5) HFMo DSSy Effect of Bandwidth Hetero- Not account for queuing ef-
(BitTorrent- geneity on download perfor- fects in the network.
like) mance. Heterogeneity band-
width can have a positive ef-
fect on content propagation.
(8) QMo(OQN) CSy,DUsy,HSy Evaluate the expected time to Do not capture all aforemen-
download a file, accounts for tioned phases of the sharing
a host of network and peer process, namely flash crowd,
level characteristics, interplay steady state. Not account the
among various critical pa- query search time (propaga-
rameters (external traffic rate, tion delay), not treated the
service variability, file popu- structured architecture.
larity...). queue type: router:
GI/G/1, Peer M/G/1/K
Table 1: comparative table of various work performance evaluation of P2P systems
REFERENCES [5] : F. Lo Piccolo, G. Neglia, G. Bianchi, ”The Effect
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