1

Exploring the Optimal Replication Strategy inP2P-VoD Systems: Characterization and

EvaluationWeijie Wu, Student Member, IEEE, and John C.S. Lui, Fellow, IEEE

Abstract—P2P-Video-on-Demand (P2P-VoD) is a popular Internet service which aims to provide a scalable and high quality service tousers. At the same time, content providers of P2P-VoD services also need to make sure that the service is operated with a manageableoperating cost. Given the volume-based charging model by ISPs, P2P-VoD content providers would like to reduce peers’ access to thecontent server so as to reduce the operating cost. In this paper, we address an important open problem: what is the “optimal replicationratio” in a P2P-VoD system such that peers will receive service from each other and at the same time, reduce the access to the contentserver? We address two fundamental issues: (a) what is the optimal replication ratio of a movie if we know its popularity, and (b)how to achieve these optimal ratios in a distributed and dynamic fashion. We first formally show how movie popularities can impactserver’s workload, and formulate the video replication as an optimization problem. We show that the conventional wisdom of using theproportional replication strategy is “sub-optimal”, and expand the design space to both “passive replacement policy” and “active pushpolicy” to achieve the optimal replication ratios. We consider practical implementation issues, evaluate the performance of P2P-VoDsystems and show how to greatly reduce server’s workload and improve streaming quality via our distributed algorithms.

Index Terms—Distributed applications, protocols, modeling, performance

F

1 INTRODUCTION

IN the past few years, we have seen a growing in-terest of using the peer-to-peer (P2P) technology to

deliver video-on-demand (VoD) services. There are al-ready a number of successful P2P-VoD services offerby companies like PPLive, PPStream and UUSee. Theadvantage of using this technology is that the system canutilize peers’ resources to satisfy other peers’ viewingneed, and thus to achieve a more scalable system ascompared to the traditional client-server architecture.The main difference between P2P-VoD systems and P2Plive streaming systems is that peers in P2P-VoD serviceneed to contribute a much larger local cache space, e.g.,physical memory and local storage so as to cache anymultimedia data, as well as their upload bandwidthto transfer data among peers. For example, in PPLivesystem [6], each peer needs to dedicate 1 GB of localstorage for the P2P-VoD service. This local storage is forcaching some previously watched movies so that in casea new peer joins the system, this peer does not needto download from the VoD content server but rather,obtains the data directly from other peers. This uniquefeature not only frees up the VoD content server toserve other peers, but more importantly, reduces theupload bandwidth traffic of P2P-VoD content providers.Since content providers usually pay ISPs based on thevolume-based charging scheme, it is to the best interest

• The authors are with Department of Computer Science and Engineering,The Chinese University of Hong Kong, Hong Kong.E-mail: {wjwu,cslui}@cse.cuhk.edu.hk

of a P2P-VoD content provider to reduce the server’supload traffic, and a proper caching policy can surelyachieve such goal. Given the distributed cache spaces ofall peers in a P2P-VoD system, the aim of our paper is toaddress how to utilize these resource efficiently so as toreduce the operating cost of a P2P-VoD content provider.Specifically, given the caching and upload capacities ofpeers, can one characterize the “optimal caching policy” soas to minimize the traffic to the P2P-VoD content server?

Different from the P2P file sharing applications, tosupport peers in a P2P-VoD service, one has to guarantee(1) a low start-up latency in accessing the movies; (2) tosupport the required playback-rate for all peers through-out their viewing sessions. To achieve these goals, a goodreplication policy should replicate enough replicas so asto support the required workload. To illustrate, considera P2P-VoD system with 100 peers and each peer offersone cache unit (i.e., let’s say each cache unit can store onemovie only). There are two movies M1,M2 with the sameviewing popularity, i.e., each with 50 viewers. Assume areplication policy keeps 99 replicas for M1 but only onereplica for M2. Then, requests for M2 will fail to findsufficient peers’ support and have to access the P2P-VoDserver. The system is caching excessive number of M1

replicas, furthermore, the system cannot take advantageof the upload bandwidth of those peers which cache M1.

It is challenging to characterize the optimal cachingpolicy in a P2P-VoD system, especially when peers havedifferent upload capacities and movies have differentviewing popularities. These factors make designing theoptimal replication policy an open problem so far. In thispaper, we address the following technical issues:

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• Given movies’ viewing popularities, what is theoptimal ratio of total storage space that should bededicated to each movie such that when a new peerarrives, it is most likely to be served by other peers?

• Given the system dynamics (e.g., peers’ churn), howto design distributed and adaptive algorithms toachieve the optimal replication ratios?

It is interesting to note that previous work [6] andconventional wisdom suggested using the proportionalreplication strategy, i.e., replicating movies proportionallyto their popularity. However, authors in [17] reporteda contradicting result that the proportional replicationmay have poor performance, especially for unpopularmovies. In this work, we give the formal justifications onthis contradiction and provide insights to the characteri-zation of the optimal replication ratios. These insightsprovide us the principles in designing practical andeffective replication algorithms. Our contributions are:• We show that proportional replication is not the op-

timal strategy. Instead, one should replicate moviesproportionally to the deficit bandwidth (we will for-mally define this concept in Sec. 2.4). The optimalreplication strategy should be more greedy for un-popular movies.

• We expand the design space by considering bothpassive and active replication. We propose a passivereplacement algorithm to decide which movie topurge when a local storage is full; we also proposean active replication algorithm to aggressively pushdata to peers so as to achieve the desired replicationratios. We evaluate our proposed algorithms andshow significant improvement of video quality andlarge reduction on server’s workload.

This paper is extended from our earlier work [20].The outline is as follows. In Section 2 we present amathematical model for P2P-VoD system and give anoptimization framework for the replication problem. InSection 3 and 4, we discuss the optimal replicationratios under the software and set-top box deploymentscenarios, respectively. In Section 5, we present our pas-sive replacement and active push algorithm to achievethe optimal replication ratios. In Section 6, we considerseveral important practical issues in implementation andpresent the performance results of our algorithms. Sec-tion 7 states the related work and Section 8 concludes.

2 SYSTEM ARCHITECTURE AND MODEL

2.1 System Architecture

We first briefly describe a general architecture of a P2P-VoD system, which mainly consists of (a) content servers,(b) trackers and (c) peers. The content servers are thesource of content and can upload data to requestingpeers. Each peer seeks to download data from the sys-tem, and in the meanwhile, it reports to the tracker thedata it caches in the local storage so as to provide uploadservice to other peers. Each video file is divided into

small pieces called chunks. When a peer joins the system,a local tracker recommends it a set of other peers fordownloading its required chunks. This peer exchangesthe buffer map with the recommended peers so thatit can determine the sources to download the requiredchunks from. Interested readers may refer to [6] for adetailed description.

In general, there are two types of deployments: soft-ware based and set-top box based. They share the similararchitecture as described above, but differ in the follow-ing. In a software deployment like PPLive or PPstream,the network is unstructured and regarded as full mesh.A peer usually contributes to others only when it isonline watching a movie. The system operator cannotcontrol any peer to be online or offline. On the otherhand, an emerging trend is to install set-top boxes (withhard-disk inside) at user’s homes and they form a P2Pnetwork. This network is usually fully connected withina local area so that a single tracker schedules the up-load/download among peers. The operator can controlthe whole network where peers are always “online” eventhough they are not watching any movie.

Formally, we define active peers to be those currentlywatching a movie and at the same time, providing up-load service to other peers, while inactive peers are thosecurrently not watching any movie but staying onlineand contributing their upload bandwidth to other peers.Hence, a software based system only consists of activepeers, while a set-top box deployment may involve bothactive and inactive peers.

In general, VoD includes various quality of services.Supporting Standard Definition (e.g., 2Mbps) or HighDefinition (e.g., 4Mbps) can be quite challenging due tothe high bandwidth requirement. Some VoD companiesrestrict these services to a limited amount of premiumusers. Some movies are of low resolution and can be eas-ily supported by other peers. Replication mainly helpsin supporting the movies with medium playback rates(e.g., 500kbps). P2P-VoD companies may also use othertechniques to partially support movies with extremelyhigh or low popularities (e.g. broadcast for very hotmovies and unicast for very cold movies). For mostmovies with popularity in the middle range, replicationstrategy needs to be carefully designed so as to alleviatethe server’s workload.

2.2 System ModelWe consider a P2P-VoD system G = {S,P,M}, where Sis the logical P2P-VoD content server of the system1, P ={P1, ..., PN} is the set of peers, and M = {M1, . . . , MK}is the set of movies stored in S. Let PA represent theset of active peers, and let Pk represent the set of activepeers which are watching movie Mk. We have Pk ⊆ PA.Similarly, denote PI as the set of inactive peers. Let uj

be the maximal upload rate ( i.e., upload capacity) of Pj .

1. A logical P2P-VoD content server may consist of many physicalservers which process any request from peers in a P2P-VoD system.

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Peers which watch movie Mk can access the data from(a) S, or (b) any other peer which is watching Mk, or (c)peers which have watched and cached Mk.

The upload bandwidth consumption of S is affectedby (a) the peer scheduling policies, and (b) movie repli-cation strategies. For the ease of presentation, we decom-pose these two design problems and use a realistic andpractical peer scheduling strategy: a peer first requestsdata from other peers, and only when other peers cannotsupply sufficient bandwidth, then this peer requests datafrom S. In here, we focus on the movie replicationstrategy and show how it can significantly impact theupload bandwidth consumption of S. Let us first statethe general P2P-VoD setting, then we give a generalmodel to show how replication strategy can affect theupload bandwidth consumption of S.

2.3 Peer Scheduling Policy

A peer scheduling strategy includes two design issues:(1) from a downloader’s viewpoint, it needs to decidewhich peers to request the data from; (2) from an up-loader’s viewpoint, it needs to decide which peers toupload the data to when it receives multiple requests.

Let us first describe how an active peer downloadsa movie. Suppose a peer wants to watch movie Mk. Ingeneral, its request can be supported by three differentsources: (a) the server S; (b) active peers which arecurrently watching the same movie Mk, and we denotethese as the concurrent peers; (c) peers which are notwatching movie Mk but have stored Mk at their localcache, and we denote these as the replication peers. Notethat a replication peer may be an active peer watchinganother movie; or an inactive peer which has movie Mk

in its cache. Lastly, in order to have a short start-uplatency and good streaming quality, each peer needs todownload the movie at its playback rate r.

In real systems, peers may perform various operationslike fast forward, rewind and replay during the viewingprocess. In this paper, we first consider a simplifiedsequential viewing model, where peers watch the moviesfrom the beginning to the end sequentially. We use thissimplification to get a neat model and show the bench-mark performance of our replication algorithms. In fact,we only need some simple modifications so as to adaptto the peer operations, which we will discuss later. Weconsider the following practical peer scheduling policy:a peer first seeks help from concurrent peers; if theplayback rate cannot be satisfied, the peer seeks helpfrom replication peers; if the playback rate still cannotbe satisfied, the server S will upload the data to this peerso as to satisfy the playback rate.

We would like to comment on the rationale of thisscheduling policy. We let S be the last requesting targetof a peer in order to reduce the upload consumptionof S so as to reduce the operating cost of the P2P-VoDsystem. Note that, in real systems, a peer may cacheonly part but not the whole movie (details are discussed

in Section 6). Therefore, requesting from a replicationpeer may result in frequent rescheduling: a peer Pi thatrequests data from a replication peer Pj needs to lookup other peers for support when Pi’s viewing part isnot cached in Pj . Concurrent peers may also performvarious operations like fast forward, rewind, replay oreven depart, however, a typical peer is more likely tostick to a movie it is interested in, so it is more likely thatPi can download from one particular concurrent peer Pk

throughout the watching period. This is why we preferconcurrent peers over replication peers to support theviewing requirement. We note that in practical systems,there might be complicated considerations on schedul-ing. Our model is not restricted in this preference; in fact,it can be easily extended to other scheduling policies.

There can be various scheduling policies regardinghow peer Pi should seek help from its concurrent peers.We would like to point out that our model is applicableto any policy that satisfies the following two properties:(a) sequentiality: only the concurrent peers that arrivedearlier than Pi can assist in the data upload for Pi; and (b)greediness: Pi downloads from earlier-arrived concurrentpeers as much as possible but not exceeding its requiredplayback rate; peers arriving later than Pi will not bereserved for uploading unless Pi’s viewing requirementis totally satisfied by the concurrent peers. Note that thesequentiality property should be satisfied in any P2P-VoD system due to the asynchronous nature of VoDsystem. The greediness property is needed because itensures the maximum efficiency of cooperation amongconcurrent peers within a swarm, which we will show inlater section. We call a scheduling policy that satisfies thegreediness property as greedy policy. Note that in a P2P-VoD system, a greedy policy allows a peer to downloadfrom earlier arrived concurrent peers in any manner, sothe scheduling policy can be easily implemented.

From an uploader’s viewpoint, it may receive mul-tiple download requests simultaneously. In our work,an active peer will serve its concurrent peers with ahigher priority. Only when its upload bandwidth is notfully consumed by concurrent peers, the active peer willprovide the remaining upload bandwidth to other peers.The rationale of the priority follows the same reasoningstated above. For an inactive peer, it will upload to thosepeers watching any movie that is stored in its local cache.The assumption is not only for mathematical tractability,but this simple scheduling rule can also maximize thenumber of peers to receive data at the playback rate r.

2.4 Model of Movie Popularity on Server’s Workload

Let us illustrate how the movie popularity can affect theserver’s upload bandwidth. First, peer Pi’s downloadrate can be supported partly by concurrent peers, partlyby replication peers, and partly by the server S. Letdc

i and dri be the total download rates supported by

concurrent peers and replication peers, respectively. Ifdc

i+dri is below the playback rate r, the server needs to fill

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up the gap r− dci − dr

i so as to satisfy the QoS guarantee.For the ease of presentation, we denote ds

i = r − dci − dr

i

(∀i ∈ PA) as the filling upload rate from the server toPi. The expected upload bandwidth consumption of theserver S is denoted as U , which can be expressed as:

U = E

( ∑

i∈PA

dsi

)= E

( ∑

k∈M

∑

i∈Pk

dsi

). (1)

Based on the peer scheduling policy above, we have:Lemma 1: In a large scale P2P-VoD system, the expectedupload consumption at the server is approximately

U ≈∑

k∈M

[E

( ∑

i∈Pk

(r − dci )

)−Rk

]+

, (2)

where Rk is the maximal upload bandwidth fromall replication peers that can contribute to Mk, or∑

i∈Pkdr

i ≤ Rk.Due to page limit, we omit all the proofs. Interested

readers may refer to the supplementary file for details.Let us define the following important notation.Definition 1: For movie Mk, we define deficit bandwidthas

Dk(nk) =∑

i∈Pk

(r − dci ) =

∑

i∈Pk

(dri + ds

i ), (3)

and letDk(nk) = E

[Dk(nk)

](4)

be the expected deficit bandwidth of having nk concurrentpeers in Pk, i.e., the bandwidth gap between the totalrequired playback rates and the total download rates thatcan be supported by nk concurrent peers. We can nowrewrite Eq. (2) and directly obtain the following lemma:Lemma 2: Given the number of concurrent peers, theexpected upload consumption at the server is

U =∑

k∈M(Dk(nk)−Rk)+. (5)

Our objective is to find a replication strategy, whichdetermines Rk, such that U , the expected upload band-width consumption of the server S, can be minimized.Thus, we want to explore how the popularity of a moviemay affect Dk(nk), which in turn will affect the choiceof replication. First we state the following lemma:Lemma 3: Under sequentiality requirement, any greedyscheduling policy minimizes the deficit bandwidth.

Lemma 3 highlights the condition that concurrentpeers can cooperate most effectively. We state an impor-tant lemma to calculate this minimum deficit bandwidth.Lemma 4: Using a scheduling policy that satisfies thesequentiality and greediness properties, deficit band-width can be iteratively calculated by

Dk(nk) = nkr −∑

i∈Pk

dci , (6)

dci =

{0, i = 1;min

(∑i−1j=1(uj − dc

j), r)

, i ≥ 2.(7)

P1 P2 P3 P4 P5 P6

ui (kbps) 500 800 200 800 300 1000dc

i (kbps) 0 500 600 400 600 500Dk(6) (kbps) 1000

TABLE 1: Example for calculating dki and Dk(nk)

Let us use an example to illustrate the above frame-work in calculating dc

i and Dk(nk). Assume six peersare watching movie Mk. These peers are P1,. . . , P6, withP1 arriving the earliest. We fix the movie playback rateat r = 600 kbps. If we know their upload capacitiesui as illustrated in Tab. 1, we can calculate dc

1, . . . , dc6

respectively, and by summing up all (r− dci ) we can get

the deficit bandwidth, or Dk(6) = 1000 kbps. This Dk(6)represents the bandwidth required to support all thesesix peers. Referring to Eq. (3), if there is no replication(or dr

i = 0), this is exactly the total upload bandwidththat the server S needs to provide.

In summary, given each peer’s upload capacity ui, onecan determine dc

i and Dk(nk). Furthermore, given theupload capacity distribution of Pk, we may determineDk(nk) by taking the expectation. Based on this frame-work, we can show how movie’s popularity impacts theupload bandwidth consumption of the server S. In latersections, we will show some interesting implications.

2.5 Discussion on Peer OperationsWe have considered the “sequential viewing” model inthe above analysis. In practice, the peers may performvarious operations (e.g., fast forward, rewind or replay)when they watch the movies. In order to adapt to thesepractical issues, we propose a revision on the systemdesign with a limited overhead on the trackers. Eachpeer reports to the tracker the chunk it needs down-loading as well as the largest chunk index it has alreadydownloaded. Denote by cd and cl the indices of thesetwo chunks. Note that cd might be smaller than cl dueto the fast forward operation, and that the set of chunksa peer caches is a subset of {1, 2, . . . , cl} since peers mayskip some parts in the middle.

We use a simple model to capture the feature. Whena peer downloads the chunk cd of a movie, the trackerrecommends a set of other peers with cl ≥ cd. Assumethat a recommended peer has a probability β to havecached this chunk. In general, β < 1 since it is possibleto have skipped this chunk before. However, β may notbe too small since a typical peer caches a large part, ifnot all, of the movie it watches.

When considering peer operations, a greedy schedul-ing policy may not minimize the deficit workload; how-ever, if the fast forward operations are rare (comparingto rewind and replay operations), a greedy schedulingpolicy is near to optimal. In later sections, we willcompute the deficit workload using this revised model.

2.6 Model of Replication on Server’s WorkloadLet us show how replication can help to reduce theserver’s workload. Intuitively, without using replication

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(or when dri = 0), Dk(nk) will be the upload bandwidth

consumption of server S for movie Mk. Replication helpsto reduce server’s upload bandwidth consumption sincepeers could use replicas to partially support the deficitbandwidth Dk(nk). For the ease of presentation, we havethe following assumptions:• We consider the system G = {S,P,M}, where P ={P1, ..., PN}, M = {M1, ..., MK}, with αN out of theN peers are active. An active peer wants to watchmovie Mk with probability ρk, with

∑Kk=1 ρk = 1.

• Each peer, either active or inactive, caches one moviethat it has watched before2.

• Peers’ upload and download scheduling policiesfollow the properties in Section 2.3.

To model the distribution of number of active peers ineach movie, one can use a closed queueing network torepresent the P2P-VoD system. Let random variable nk

denote the number of peers watching movie Mk. Similarto the work in [18], we can express the probability formovie Mk having nk viewers, for k = 1, 2, . . . , K, as:

P (n1 = n1, . . . , nK = nK) = (αN)!ρn11

n1!. . .

ρnK

K

nK !, (8)

with∑K

k=1 nk = αN . Here, ρi implies the relative pop-ularity of movie Mi. Based on this queueing model, wehave the following proposition:Proposition 1: The average upload consumption of S is

U(q) =∑

∑nk=αN

{(αN)!

ρn11

n1!. . .

ρnK

K

nK !×

∑

k∈M

[Dk(nk)−

qk

∑

l∈M(Cu

l (nl) +Dl(nl)− nlr)− qkCuI ((1− α)N)

]+}

, (9)

where qk is the fraction of cache space dedicated to Mk,Cu

l (nl) = E(∑

i∈Plui

), Cu

I (nI) = E(∑

i∈PI ui

).

Now the model of the optimal replication strategy can beformulated as follows. We seek to find a set of replicationratios q which satisfies:

minq

U(q)

subject to qT · 1 = 1. (10)

In other words, we want to determine the number ofreplicas for each movie Mk ∈ M, so that the averageupload bandwidth consumption of S can be minimized.

In general it is difficult to get a close form solution forthis optimization problem. However, as we will show inthe following section, when we consider some commondeployment cases, one can get some interesting implica-tions and insights in designing replication strategies.

2. In general, a peer may also cache multiple movies. In suchsystems, the optimal caching policy is coupled with the optimalscheduling strategy and is hence hard to decide due to the NP-hardnessof scheduling strategy. Nevertheless, note that the typical cache size ofa peer is 1 GB (e.g., in PPLive), and typical movie size is about 500 MB.Thus, we assume that besides the currently watching movie, an activepeer can cache one extra movie so as to cope with typical settings ofreal systems.

3 OPTIMAL REPLICATION IN SOFTWARE DE-PLOYMENT SCENARIO

In this and the next section, we discuss two typicaldeployment scenarios for P2P-VoD services. These sce-narios have different fraction of active peers and theywill affect the replication policies.

3.1 Deployment Scenario and Operation ModesRecall the previous section, the two typical deploymentscenarios we consider are software and set-top box de-ployment. In general, under the software deploymentscenario, the fraction of active peers, or α, is close to 1.On the other hand, under the set-top box deploymentscenario, α can take on value in [0, 1] and may besignificantly less than 1. The fraction of active peerscan greatly influence the optimal replication strategy. Inorder to further analyze any P2P-VoD system, we definetwo operating modes as follows:• Deficit mode: the average upload capacity of all peers

is less than the playback rate of a movie, i.e., u < r.• Surplus mode: the average upload capacity of all

peers is larger than the playback rate of a movie.In addition, we further divide it into two modes(a) slightly-surplus mode, i.e., u & r, and (b) highly-surplus mode, i.e., u >> r.

3.2 Server’s workload in Software Deployed Sys-temsIn this subsection, we derive the server’s workload forsoftware deployment scenario where all peers in thesystem are active, i.e., α = 1. Note that the deficit modeis not a rational operating point for a software P2P-VoDsystem where replication can rarely help. To see this,we know that under the deficit mode, we have u < r.The server’s total upload bandwidth consumption tosupport all peers is N(r − u), where N is the numberof peers in the system. When N increases, the server’sbandwidth consumption will become very large as itincreases linearly with N . Meanwhile, the upload band-widths of peers are all used up to support concurrentpeers, and thus no replication strategy can help to reducethe workload in S. The only way to reduce the workloadin S is to lower the playback rate r so that the systemcan be in the surplus mode.

On the other hand, when the system is in the surplusmode, replication is not always necessary. For a systemoperating in the highly-surplus mode, concurrent peerscan support each other with ease. In other words, theabundance of peers’ upload bandwidth makes repli-cation unnecessary. This abundance in resource willmotivate the P2P-VoD system designer to increase theplayback rate r so as to improve video quality by betterutilizing peers’ resources, which eventually brings thesystem to the slightly-surplus mode.

To summarize, the only interesting case for the softwaredeployment is when the system is operating at the

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bandwidth (kbps) 768 384 256 128share 50% 30% 5% 15%

TABLE 2: Peers’ upload capacity distribution

slightly-surplus mode. As we will show, designing anoptimal replication strategy is a non-trivial task.

Under the software deployment scenario, by settingα = 1 in Eq. (9), we have the following proposition:Proposition 2: In software deployment, the average up-load bandwidth consumption at the server S is:

U(q) =∑

∑nk=N

{N !

ρn11

n1!. . .

ρnK

K

nK !·

K∑

k=1

[Dk(nk)−

qk

K∑

l=1

(Cul (nl) +Dl(nl)− nlr)

]+}

. (11)

3.3 Characteristics of Deficit BandwidthTo minimize U , the decisions on qk are highly dependenton the shape and characteristics of Dk(nk). Let us con-sider some typical distributions (e.g., uniform, normal,. . .) to represent peers’ upload capacity so as to gain adeeper understanding. In addition, we also use numer-ical and fitting methods to show the characteristics ofDk(nk). In here, we present some typical examples.Example 1: (Exploring the characteristics of Dk(nk)):Assume nk peers are watching movie Mk, and the movieplayback rate is r = 500 kbps. Fig. 1 illustrates theimpact of movie popularities on the deficit bandwidthDk(nk) when we vary the nk ∈ [1, 100]. In Fig. 1(a),the peers’ upload capacity is normally distributed withaverage of 540 kbps and variance 200. It shows thatDk(nk) is concave in nk and can be fitted into the formDk(nk) = D0 − Ae−λ(nk−n0). In Fig. 1(b), we set a morerealistic bandwidth distribution according to [4]. Theupload capacity distribution is illustrated in Tab. 2. InFig. 1(c), we still use this bandwidth distribution, andwe consider the impact of user operations. We assumethat due to this effect, when a peer seeks help from aconcurrent peer, it has a probability 0.8 to successfullyfind the chunk needed. The deficit bandwidth Dk(nk)shows very similar trend as the previous figures, butonly differs in that the deficit workload is a bit largercompared to Fig. 1(b). We omit the similar cases that westudied, but they all imply the following observation:Observation 1:• Dk(nk) is a concave function on movie popularity nk,

and it converges to a fixed value when nk approachesinfinity.

• The convergence rate of Dk(nk) increases with the aver-age of upload capacity and decreases with the variance.

Physical meaning: The concavity and convergence fea-tures imply that for unpopular movies, they have amuch higher marginal increase on the deficit bandwidthDk(nk) while for popular movies, the marginal increaseon Dk(nk) is minimal. An intuitive explanation of thisfeature is that peers within a larger set can cooperatemore effectively and thus achieve higher utilization of

peers’ upload bandwidth. Using law of large number onEq. (7), for large enough i, we have

∑i−1j=1 uj ≈ (i − 1)u

with high probability. Furthermore, if we assume u > rand i > r/(u− r) + 1, then we have

dci ' min

(i−1)u−

i−1∑

j=1

dcj , r

≥ min ((i−1)(u−r), r) = r,

which means that any late arriving peer can receivesufficient download from concurrent peers and will notincur any bandwidth consumption on S.

The above analysis shows the reason why deficitbandwidth Dk(nk) is sub-linear. This also implies thatthe conventional wisdom of using the proportional repli-cation strategy, or caching the more popular movies [6],[21], [22], is sub-optimal. Looking at Fig. 1, we see that apopular movie with 25 viewers needs nearly the samedeficit bandwidth as a movie with 100 viewers, while anunpopular movie of five viewers needs more than halfof the deficit bandwidth as compared with a popularmovie with 100 viewers.

3.4 Characterizing the Optimal Replication StrategyNow the impact of movie popularities on server’s work-load is clear: without replication, the server’s workloadfor movie Mk is simply Dk(nk). The goal of replication isto reduce the workload on S. The non-linearity of Dk(nk)implies one should be greedy in replicating unpopularmovies. In the following, we use examples to justify ourargument, and at the same time, determine the optimalreplication ratios q.Example 2 (Sub-optimality of the proportional repli-cation strategy): Assume that the system consists ofN = 600 active peers and K = 25 movies. Movie M1

- M5 are popular movies while movie M6 - M25 areunpopular. Peers choose each of the popular movies witha probability of ρpop = 1/6, or each of the unpopularmovies with a probability of ρunpop = 1/120. The play-back rate is set at r = 500 kbps, Peers’ upload capacityfollows Tab. 2.

Denote qunpop as the fraction of cache space (which canstore 600 movies) of caching any unpopular movie (M6

- M25), and 1− qunpop as the fraction of caching popularmovies (M1 - M5). We develop a simulator to explore thereplication strategy. In particular, we vary the fraction ofcache space that is used to store unpopular movies from0% (i.e., all cache space is used to store popular movies)to 100% (i.e., all cache space is used to store unpopularmovies), and evaluate the system performance. Fig. 2illustrates the upload bandwidth consumption on theserver when we vary qunpop.

If the system only replicates popular movies, then alldeficit bandwidth Dk of unpopular movies will con-tribute to the server’s workload. This corresponds tothe first point from the left (about 15 Mbps) in Fig. 2.Similarly, if all replications are for unpopular ones, theserver’s workload is around 6 Mbps and this corre-sponds to the last point at the right of the figure. Since

7

0 20 40 60 80 1000.4

0.6

0.8

1

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defic

it ba

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idth

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bps) numerical result

fitting result

Dk(n

k)=1.13−0.54e−0.07(n

k−0.72)

(a) upload capacity: normal distributionwith average 540 kbps and variance 200.

0 20 40 60 80 1000.4

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Dk(n

k)=1.36−0.75e−0.04(n

k−0.16)

(b) upload capacity: discrete distributionin Tab. 2.

0 20 40 60 80 1000.4

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bps)

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Dk(n

k)=1.68−1.01e−0.06(n

k−0.45)

(c) upload capacity: discrete distributionwith peer operations.

Fig. 1: Deficit bandwidth Dk vs. nk

0 20 40 60 80 100

2

4

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8

10

12

14

fraction of caching unpopular movies

serv

er’s

wor

kloa

d (M

bps)

proportionalreplication

optimal replication

Fig. 2: Replication impact on server’s workload in asoftware-deployed system, where r = 500 kbps.

popular moderate unpopularproportional fraction 71% 14% 14%

optimal replication fraction 18% 32% 50%deficit bandwidth fraction (qk) 21% 30% 49%

TABLE 3: Optimal replication vs. popularity fractions

5/6 fraction of the requests are for popular movies, usingthe proportional replication strategy, only 1/6 or 17% of thecache space should be dedicated to store the unpopularmovies. From the figure, we see that the workload onthe server will be around 10 Mbps. However, the optimalreplication fraction for unpopular movie should be around70% where the server’s upload bandwidth consumptionis less than 2 Mbps. This simple example validates thefollowing observation:Observation 2: In a software-based system, proportionalreplication is far from optimal and incurs a higher server’sworkload as compared with the optimal replication strategy.Example 3 (Exploring optimal replication ratio): Weconsider a P2P-VoD system with 700 peers and 35movies. M1 - M5 are popular movies with ρpop = 1/7; M6

- M15 are moderately popular movies with ρmid = 1/70;while M16 - M35 are unpopular movies with ρunpop =1/140. We simulate this system and explore the server’sworkload at each possible integral fraction combinationq ∈ {(qpop, qmid, qunpop) : qpop + qmid + qunpop = 100%}.Using exhaustive search, the popularity fractions and op-timal replication fractions of different movies are shownin Tab. 3. Obviously, the optimal replication strategyshould be “aggressive” in caching unpopular movies.

It is mathematically difficult to derive the optimalratios of replication from the optimization problem, andone cannot afford to use exhaustive search for large scale

P2P-VoD systems. However, we obtain an interestingfinding: the optimal ratio for replication for movie Mk

should be close to the fraction of deficit bandwidthDk(nk) for movie Mk among the total deficit bandwidth,i.e., let

qk =Dk(nk)∑Ki=1Di(ni)

, (12)

then we haveqoptk ' qk. (13)

For instance, in the above example qpop = 21%, qmid =30% and qunpop = 49%, which are near to the optimalratios for replication. This example reveals the followingobservation:Observation 3: Proportional deficit bandwidth replication isa good estimate to the optimal replication ratios.

Our model can be easily extended to heterogeneousplayback rates of movies. Further, Observation 3 stillholds for this case. Due to page limit, we omit the details;interested readers may refer to the supplementary file.

Examples using other typical settings all stronglysupport our observations. We like to point out thatthere is an intuitive explanation to the above resourceallocation strategy: without replication, Dk(nk) is exactlythe server’s bandwidth consumption for movie Mk, andthus, allocating remaining bandwidth in this ratio is themost efficient method to balance each movie’s requestload to the server S. This idea leads to the replicationalgorithm which we will discuss in the next section.

4 OPTIMAL REPLICATION IN SET-TOP BOXDEPLOYMENT SCENARIO

In the set-top box deployment scenario, peers are alwaysonline even when they are not watching any movie. Inother words, α might be significantly less than 1. Theexistence of inactive peers greatly changes the systemdesign. Since the number of downloading peers maybe significantly less than uploading peers, therefore, theplayback rate of movies could be set higher comparedwith the software based deployment. For example, ifonly half of the total N peers in the system are watchingmovies, then total available upload bandwidth frompeers is still uN , while the total download requirement

8

is r ·N/2. Thus, the server can work with low workloadif r is set no larger than 2u. For better quality of service,VoD providers have incentive to increase the playbackrate as high as possible, or r ' 2u. In this case, the movieplayback rate is usually larger than the average uploadcapacity.

Since the playback rate is larger than the averageupload bandwidth, an active peer is unlikely to haveremaining bandwidth after serving concurrent peers. Inother words, nearly all the replication peers are inactivepeers, so

U(q) '∑

∑nk=αN

{(αN)!

ρn11

n1!. . .

ρnK

K

nK !

K∑

k=1

[nk(r − u)− qkCu

I ((1− α)N)]+}

. (14)

Fig. 3(a) illustrates this scenario with r = 1.1 Mbpsand the peer’s upload capacity follows Tab. 2. From thefigure, we can see that the deficit workload Dk(nk) islinear in terms of nk, or

Dk(nk) ' nk(r − u). (15)

Intuitively, since the deficit bandwidth of concurrentpeers is linear in terms of the movie popularity, weshould replicate a movie proportionally to its popularity.However, since the statistic of estimating the popularityof an unpopular movie has a higher variance, one shouldbe a bit more “greedy” in replicating unpopular movies.We use an example to support this claim.Example 5 (Optimal replication in a set-top box sys-tem): The setting of this example is similar to Example 2,but the differences are that we add 600 idle peers, i.e.,α = 0.5, and increase the playback rate to r = 1.1 Mbps.Fig. 3(b) shows total workload of the server with respectto qunpop. The optimal value for qunpop is around 22%, abit larger than the fraction of unpopular movie viewers(17%). This result validates the above argument.

Note that the replication ratios in Observation 3 isstill a good estimate to the optimal replication ratio. Inthis example, qpop = 81% and qunpop = 19%, where theserver’s workload is near the minimum.

Last but not least, comparing this result with that inprevious examples, we can conclude that the optimalreplication strategy is very different for the software de-ployed and the set-top box deployed P2P-VoD systems.

5 ALGORITHMS TO CONTROL REPLICATIONRATIOS

Let us present several algorithms to achieve the optimalreplication ratio q in a P2P-VoD system. Note that aP2P-VoD is with high churn, therefore, the replicationalgorithms need to be robust and efficient in minimizingthe server’s workload. In general, there are two ways tocontrol or adjust the replication ratios:

Algorithm 1 Replacement Algorithm1: for any peer that starts to watch a new movie do2: if this movie is already stored in its local cache

then3: do not replace any movie;4: else5: for each movie Mi in its local cache do6: calculate the expected # of caches for Mi:

Nexpi = [Di(ni)N ] /

∑k Dk(nk);

7: calculate the current # of caches for Mi: N curi ;

8: calculate the satisfaction index for Mi:SIi = N cur

i /Nexpi ;

9: end for10: replace the movie with the highest SIi.11: end if12: end for

• Passive adjustment: peers adjust the replicationratio in the P2P-VoD system using replacement al-gorithms, i.e., when a peer’s local cache is full, itdecides which movie(s) to purge so as to accom-modate a new movie that can reduce the server’sworkload;

• Active adjustment: the server S and all peers ac-tively push out (or upload) data for which thereplicas are not at the desired replication ratios.

5.1 Passive Adjustment via Replacement Algorithm

When the cache space of a peer is full, a peer has todecide which movie(s) to purge from the cache spacesuch that new movies could be cached. Since we want toexplore the impact of movie popularities to the server’sworkload, we consider replication algorithms that re-place the whole movie, instead of partial replacement.Nevertheless, generalization can be easily made.

Previous work [6] suggested a weight-based evalua-tion scheme, or replicating proportionally to a movie’spopularity. Our previous examples already show thesub-optimality of such replication algorithm and oneshould replicate movie proportionally to its deficit band-width. This leads to the following replacement algorithm,which is illustrated in Algorithm 1.

The main idea behind this algorithm is to keep thenumber of replicas proportional to the deficit bandwidth.We define satisfaction index (SI) to express the extent thata movie has enough replicas. When SIk < 1, it meansthat the number of replicas for movie Mk is below thedesired replication ratio. On the other hand, if SIk > 1,the number of replicas of Mk exceeds the desired ratio.Therefore, in each round, we purge the movie that hasthe highest SI from the local cache.

The idea of the algorithm is derived from the opti-mization framework. The objective of replication is tominimize U . Noting Eq. 8, the distribution of peers ineach movie is centered around nk = Nρk,∀k. RecallingProposition 1, if we set qk = ρk (which is the objective of

9

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def

icit

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serv

er’s

wo

rklo

ad (

Mb

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optimal replication

(b) Replication impact on server’s work-load

Fig. 3: Replication in set-top-box system, where r = 1.1 Mbps, upload capacity distribution follows Tab. 2

Algorithm 2 Push Algorithm1: while system is in an idle time slot do2: find out a list of replication peer candidates which

will most likely be inactive at the publishing in-stance;

3: estimate the total volume available for push4: calculate the total volume desired for coming-to-

hot movies: ∑k Dk(nk)× (movie length)

5: if total available volume is larger than desiredthen

6: assign each movie Mi with the volume it desires;7: else8: for each movie Mi do9: assign volume

Di(ni)∑k Dk(nk) × (total available volume)

to the list of replication peer candidates;10: end for11: end if12: end while

Algorithm 1), then we can minimize∑K

k=1

[Dk(Nρk) −Rk(n, qk)

]+, and can hence approximately minimize theaverage workload of the server in Eq. 9.

Although requiring global information, this algorithmis efficient in practice. Each peer reports to the trackerthe current cached movies, and the tracker can calculatethe satisfaction indices and broadcast to all peers. Thesecan be done in a proper frequency (e.g., once in fiveminutes), and thus the overhead can be minimal. It isalso worth noting that this frequency cannot be too low,otherwise, some movies will oscillate between high andlow satisfaction indices and the system cannot converge.In Sec. 6, we evaluate the impact of delay in broadcastingSI and show the convergence of the system.

5.2 Active Adjustment via Push Strategy

Our proposed replacement algorithm can reduce theserver’s workload, other factors still constrain the systemperformance. For instance, the server’s workload maydramatically increase when a popular movie is newly

released, since there will be a sudden surge of demandbut only few peers in the system have cached this movie.By simply relying on the replacement algorithm, thesystem will take a long time to converge to the optimalreplication ratios. To overcome this limitation, one cantake a proactive approach to push out a movie if weknow that it will be a popular object. This leads to thepush algorithm as depicted in Algorithm 2. In essence,the push algorithm utilizes the excessive bandwidth inidle time slots to push some data for future use soserver’s workload could be “flattened” over time. Thisalgorithm causes an overhead at the server. During atime period, the server incurs an extra upload consump-tion of Nor if it pushes the data to No peers. In the nextsection, we will show that this overhead can be minimalif we limit the number of peers to push the data to.

Predicting the dynamics of movie popularity is impor-tant in our push algorithm, but is difficult in general.One important feature is the “daily periodicity” [6], i.e.,most peers access the network every evening, and thisis in particular true for TV series. We can take this advan-tage and proactively replicate the content in the daytime.The authors in [11] discussed popularity prediction ina P2P-VoD setting using time-series analysis techniques.Besides periodicity, the movie content also plays a majorrole. An accurate prediction on the popularity dynamic isstill a challenging research topic and is beyond the scopeof this paper. In the following section, we assume thepopularity dynamics is known a priori and present theperformance results on using our proposed algorithms.

Our push algorithm shares the similar idea proposedin [14], which considers homogeneous peers with thesame upload bandwidth and storage space. In this work,the authors evaluate the system performance when therequest arrival rate is low, i.e., the system is in the highlysurplus mode. Hence, the system performs well eventhough each video has only one replica. In contrast,by carefully calculating the number of replicas for eachvideo, our design can support a higher playback ratewhere the total upload bandwidth from all peers isslightly larger than the total download requirement. Wedo not compare the performance of the two approachesdue to the different system settings.

10

6 PERFORMANCE EVALUATION

6.1 Performance of Replacement AlgorithmWe carry out extensive simulation to validate our modelsand evaluate the performance of our proposed replace-ment algorithm. We consider a software-based P2P-VoDsystem where α = 1. Unless otherwise specified, we usethe following as inputs to our simulator:• The system contains N = 10, 000 active peers. Peer’s

upload capacity distribution follows Tab. 2, withaverage of 531 kbps.

• The system provides K = 250 kinds of movies. Eachmovie is with the playback rate of r = 500 kbps.

• Movie popularity follows a Zipf distribution [13]with parameter γ = 1.

• At each round, an active peer requests a movie.Active peers switch movie channel every round.

The movie playback rate and average upload capacitywe set are based on realistic settings like PPLive. Thetracker in the system records the current cache distribu-tion in the system and that all peers can use this informa-tion to do replacement. We compare server’s workloadusing the following replacement algorithms: (a) Ourproposed algorithm, which keeps replicas proportional todeficit bandwidth; (b) Proportional algorithm, which keepsthe replicas proportional to movie popularity; (c) First-in-First-out (FIFO) algorithm, which keeps the newly cachedmovie and purges the oldest one.

Fig. 4 illustrates the comparison of the proportionalreplica distribution vs. the optimal replica distribution(both normalized to 1). We use γ = 1 as the default valueunless otherwise specified, and arrange the movies in adecreasing order of popularity. Our proposed algorithmkeeps fewer popular movies than the proportional dis-tribution and is more greedy in replicating unpopularmovies. Thus, the optimal replica distribution is “flatter”than the proportional distribution.

Fig. 5 compares the server’s workload using differentreplacement algorithms. We record the server’s load afterround 20 since we are interested in the steady stateperformance. In Fig. 5(a), the server’s average workloadis around 9 Mbps using our proposed replacement algo-rithm, but is 75 Mbps using the proportional algorithmor 74 Mbps using the FIFO algorithm. Hence, our pro-posed push algorithm reduces the server’s workload bya factor of eight. In Fig. 5(b), we add into user interactions,i.e., peers may perform various operations, and has aprobability β = 0.8 of having the chunk requested bya concurrent peer. We recompute the deficit workloadand decide the replication ratios, which shows a similarreduction on server’s workload.

We also evaluate the performance of algorithms underdifferent system parameters. Due to the page limit, wepresent our simulation results in the supplementary file.

Another important performance measure is the num-ber of peers which can watch movie at the normalplayback rate r (which we call satisfied peers) when givena finite server upload capacity. We set the simulation

environment as the previous case and the server uploadcapacity is restricted at 10 Mbps. Fig. 5(c) shows thecomparison on fraction of satisfied peers using differentreplacement algorithms. From the figure, our proposedreplacement algorithm can ensure the maximum ratioof peers that can watch the movie at the playback rate,achieving approximately 100% of satisfied peers, whilethe ratio is around 96% when using the proportional orFIFO algorithm. These results validate that our proposedreplacement algorithm can reduce the server’s workloadand at the same time, improve streaming quality.

We also considered practical issues on implementa-tions, e.g., the delay of broadcasting information fromthe tracker, replacement based on incomplete informa-tion, the impact of multiple cache space and the peerdeparture. Due to the page limit, we present the evalu-ation the system performance in the supplementary file.

6.2 Performance of Push AlgorithmIn here, we show that the proposed push algorithm cansignificantly improve the system performance, particu-larly for a set-top box deployed system. The key ideais to push some data to some inactive peers in advancesuch that the server’s workload could be flattened downwhen publishing a new popular movie. The simulationsetting is similar to the previous one but the differencesare:• There are 5,000 active peers and 5,000 inactive peers.• Playback rate of a movie is doubled to r = 1.0 Mbps.• Initially there are K = 249 kinds of movies{M1,...,M249} with a Zipf popularity distribution(γ = 1). At the beginning of round tp, a new popularmovie M250 is published. The popularities of these250 movies follow a new Zipf distribution and M250

is the most popular one.Movie M1 - M249 can be stored in local cache of active

and inactive peers. In a traditional system, before roundtp, M250 will not be in any local cache since no peerrequests this unpublished movie. Hence, the system willhave a very heavy workload at the publishing instance.With the push strategy, the new movie M250 can bepushed into inactive peers’ cache before being published.We divide a day into 24 rounds (1 hour/round), ofwhich we allow 18 rounds in advance to push a newmovie before the publication. To avoid introducing muchoverhead, in each round we only push the data of thisnew movie into forty inactive peers. At tp = 19, the newmovie is published. After the publishing instance of thenew movie, we do not push the data any more.

Fig. 6 illustrates the improvement using the push strat-egy. With a limited overhead, this strategy can signifi-cantly decrease the server’s workload at the publishinginstance of a new movie. In other words, this allowsthe system to “prepare” the data ahead of the flashcrowd event. In comparison, the system without usingthe push strategy will experience heavy workload notonly at the time of the new movie publication, but also

11

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uti

on

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0 50 100 150 200 2503

4

5

x 10−4

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repl

ica

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ribut

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Fig. 4: Proportional vs. optimal replica distribution

20 40 60 80 1000

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tio

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Fig. 5: Comparison of replacement algorithms

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Fig. 6: Performance improvement using push strategy

in the following rounds after publishing the movie, as itis slow to adjust to the optimal replication ratio.

7 RELATED WORK

Replication has long been an effective strategy to im-prove performance in P2P systems. Existing literatureshave different objectives and hence lead to different con-clusions. Kangasharju et al. [7] studied how to replicateP2P content distribution systems so as to optimize fileavailability. The main result is the logarithmic replicationrule which states the number of copies for a file shouldbe proportional to the logarithm of file popularity. Linet al. [9] formulated the replication problem as an op-timization problem and compared the performance ofseveral decentralized algorithms in terms of improvingfile availability. They showed each algorithm has anadvantage depending on system parameters. Tewari etal. [16] claimed that in P2P networks, proportional repli-cation is optimal in terms of minimizing the averagenumber of links traversed to a download. They showedthat the least-recently-used (LRU) algorithm automat-ically achieves near-proportional replication. Cohen etal. [3] discussed the optimal replication to improve the

effectiveness of blind search in a decentralized unstruc-tured P2P network. They showed that uniform and pro-portional replication yield the same performance whilethe optimal lies in between them. Leukopoulos et al.[10] proposed a hybrid Genetic Algorithm to study thedata replication for given current replica distribution.Khan et al. [8] compared ten static heuristic Internet datareplication algorithms so as to give insight the selectionof a particular algorithm to be used in a given scenario.

Recent popularity of P2P-VoD systems leads to therethinking of replication. Previous replication algorithmsare not suitable due to a very different objective: tominimize the server’s workload. However, early worksin P2P-VoD did not address this issue. Authors in [4],[5] showed the benefit of a peer-assisted VoD systemby utilizing peers’ upload bandwidth. The deploymentwas restricted to single video approach, i.e., peers onlyredistribute content to concurrent peers and hence thereis no real replication. Huang et al. [6] did original re-search in the design and implementation of a real P2P-VoD system. The multiple movie cache scheme revealedthe possibility of replication, and showed reduction onserver’s workload. However, the weight-based replace-ment algorithm, which replicates movies proportionallyto popularity, was reported to have poor performancefor unpopular movies in [17]. Similar proportional repli-cation strategies were also implemented in [21], [22].

Recently some work focused on replication for P2PVoD systems. Poon et al. [12] reformulated the replica-tion problem in terms of minimizing server’s workload.Cheng et al. [2] proposed and evaluated a heuristic algo-rithm of lazy replication. These two works were basedon simulations but did not provide theoretical analysis.Tan et al. [15] discussed content placement for a P2P-

12

VoD system. Wu et al. [19] used dynamic programmingto derive the optimal replacement strategy for P2P-VoDsystem. These two works assumed homogeneous up-load capacity, which is different from our model whichconsiders peer heterogeneity. Besides, our model differ-entiates concurrent peers and replication peers whichis different from [19]. Chen et al. [1] considered pre-fetching strategy for a peer-assisted IPTV system basedon a structured IPTV platform, which is different fromunstructured P2P systems.

8 CONCLUSION

Movie replication is an effective technique in the de-sign of P2P-VoD systems. However, it remains an openproblem to answer what the optimal replication policyshould be so as to minimize the server’s workload.In this paper, we present mathematical models andformulate an optimization framework to understand theimpact of movies’ popularities on server’s workload,and reveal important principles in designing optimalreplication algorithms. We show that conventional pro-portional replication strategy is far from optimal; rather,one should be more “aggressive” to replicate unpopularmovies. Furthermore, to operate the system at the op-timal point, we propose both passive replacement andactive push strategies. Our algorithms are effective evenunder a dynamic environment (e.g., with peers arrivingor leaving the P2P-VoD system) and movies with differ-ent playback rates. We discuss practical implementationissues and validate via extensive simulations to showthat we achieve high QoS guarantee in streaming and atthe same time, reduce workload at the server.

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[2] B. Cheng, L. Stein, H. Jin, and Z. Zhang. A framework for lazyreplication in p2p vod. In Proc. of NOSSDAV, 2008.

[3] E. Cohen and S. Shenker. Replication strategies in unstructuredpeer-to-peer networks. In Proc. of ACM SIGCOMM, 2002.

[4] C. Huang, J. Li, and K. W. Ross. Can internet video-on-demandbe profitable? In Proc. of ACM SIGCOMM, 2007.

[5] C. Huang, J. Li, and K. W. Ross. Peer-assisted vod: Makinginternet video distribution cheap. In Proc. of IPTPS, 2007.

[6] Y. Huang, T. Z. Fu, D.-M. Chiu, J. C. S. Lui, and C. Huang.Challenges, design and analysis of a large-scale P2P-VoD system.In Proc. of ACM SIGCOMM, 2008.

[7] J. Kangasharju, K. Ross, and D. Turner. Optimizing file availabilityin peer-to-peer content distribution. In Proc. of IEEE INFOCOM,2007.

[8] S. Khan and I. Ahmad. Comparison and analysis of ten staticheuristics-based internet data replication techniques. Journal ofParallel and Distributed Computing, 68(2):113–136, 2008.

[9] W. Lin, C. Ye, and D.-M. Chiu. Decentralized replication algo-rithms for improving file availability in P2P networks. In Proc. ofIWQoS, 2007.

[10] T. Loukopoulos and I. Ahmad. Static and adaptive distributeddata replication using genetic algorithms. Journal of Parallel andDistributed Computing, 64(11):1270–1285, 2004.

[11] D. Niu, Z. Liu, B. Li, and S. Zhao. Demand forecast andperformance prediction in peer-assisted on-demand streamingsystems. In Proc. of IEEE INFOCOM, pages 421–425.

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[13] T. Qiu, Z. Ge, S. Lee, J. Wang, Q. Zhao, and J. Xu. Modelingchannel popularity dynamics in a large iptv system. In Proc. ofACM SIGMETRICS, 2009.

[14] K. Suhy, C. Dioty, J. Kurosey, L. Massoulie, C. Neumann,D. Towsley, and M. Varvello. Push-to-peer video-on-demandsystem: Design and evaluation. IEEE JSAC, 25(9):1706–1716, 2007.

[15] B. Tan and L. Massoulie. Brief announcement: adaptive contentplacement for peer-to-peer video-on-demand systems. In Proc. ofACM PODC, 2010.

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Weijie Wu is working towards his Ph.D. degreein the Department of Computer Science & En-gineering at The Chinese University of HongKong. He is doing research in the Advanced Net-working and System Research Group, under thesupervision of Prof. John C.S. Lui. His currentresearch interests include P2P networks andnetwork economics. Before coming to CUHK, heobtained his Bachelor’s degree from School ofElectronics Engineering and Computer Science,Peking University in July 2008.

John C.S. Lui was born in Hong Kong and iscurrently a professor in the Department of Com-puter Science & Engineering at The ChineseUniversity of Hong Kong. He received his Ph.D.in Computer Science from UCLA. His currentresearch interests are in communication net-works, network/ system security (e.g., cloud se-curity, mobile security, etc), network economics,network sciences (e.g., online social networks,information spreading, etc), cloud computing,large scale distributed systems and performance

evaluation theory. John serves in the editorial board of IEEE/ACMTransactions on Networking, IEEE Transactions on Computers, IEEETransactions on Parallel and Distributed Systems, Journal of Perfor-mance Evaluation and International Journal of Network Security. Johnwas the chairman of the CSE Department from 2005-2011. He receivedvarious departmental teaching awards and the CUHK Vice-Chancellor’sExemplary Teaching Award. He is also a corecipient of the IFIP WG7.3 Performance 2005 and IEEE/IFIP NOMS 2006 Best Student PaperAwards. He is an elected member of the IFIP WG 7.3, Fellow of ACM,Fellow of IEEE and Croucher Senior Research Fellow. His personalinterests include films and general reading.