Missing Piece Issue and Upload Strategies in Flashcrowds and P2P-assisted Filesharing

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1 Missing Piece Issue and Upload Stategies in Flashcowds and P2P-assisted Fileshaing Fabien Mathieu FT R&D 38, ue du généal Leclec Issy le Moulineaux Fance Julien Reynie Goupe TREC, ENS 45, ue d Ulm 755 Pais Fance Abstact Pee-to-pee netwoks povide bette scalability fo the fileshaing applications they undelie. Unlike taditional seve-based appoach such as FTP, maintaining a constant QoS with a fixed numbe of seves seems feasible, whateve the numbe of pees involved. Howeve, a P2P fileshaing netwok sometimes happens to satuate, notably in a semi-p2p fileshaing achitectue o duing flashcowds phase, and scalability may fail. Even smat netwoks can encounte the whole file but one piece downloaded case, which we call stavation. We suggest a simple and vesatile fileshaing model. It applies to all pieces-oiented fileshaing potocols used in softwaes such as MlDonkey o BitToent. Simulations of this model show that stavation may occu even duing flashcowds. We popose a theoetical explanation fo the so-called stavation phenomenum. 1 Intoduction A P2P file-shaing netwok is an inteface pemitting data exchange between uses aiving and depating independently. P2P netwoks aise a wide-ange of subjects to study, including dynamic management of P2P ovelay netwoks [1, 12], publication and seach of shaed content [6, 2] o analysis of effective download capacity [4, 11, 9, 7]. The downloading efficiency is cucial, as it is one of the main chaacteistics most people would conside to choose a P2P netwok athe than anothe. In this pape we focus on the unfinished download case. This poblem may aise when downloading one s favoite Linux distibution using, fo efficiency easons, a file-shaing softwae such as MLDonkey [3] o BitToent [1]. The undelying potocols divide files into smalle pats that ae often called pieces o chunks. This allows pees to begin shaing content as soon as they have one piece. Imagine that afte a shot while, you have obtained the whole file except one piece and you ae waiting fo you download to be completed. This may be long, vey long, o could simply neve happen. We call this phenomenum stavation. Section 2 intoduces elated wok and biefly descibes ou appoach and ou modeling assumptions. Section 3 shows inteesting elated esults obtained by means of simulations of the model. In Section 4 we pesent stability esults fo ou famewok. This povides some insight into the stavation issue in eal file-shaing netwoks. Section 5 compaes diffeent upload stategies and gives chaacteistics of safe states, whee data can suvive as long as needed... 2 Model Fileshaing has been peviously modeled in diffeent ways. Fo instance, [4] uses a multiple class closed queuing netwok. Heein we study the fileshaing of a single file in an highly connected ovelay netwok, which is often called swam. We implicitly assume that a seve, which does not possess the file, coodinates the uses. This assumptions match well BitToent potocol, as uses must connect to a so-called tacke to paticipate. Pees coespond to P uses that want to download the file, and that can potentially shae patial content. Seeds ae S uses that shae the whole file. We denote by K the numbe of pieces the file is split into. These pieces can be downloaded independently. This simple famewok has fist been poposed by [11]. [9] extended it to a fluid model, and [7] offeed some mathematical esults about stability of such systems. The pesent pape diffes fom elated wok on an impotant point: we choose an Upload-oiented Appoach (UA) athe than a Download-oiented Appoach (DA). This means in simple tems that fo us, using UA, the sende choses which piece to send to whom wheeas in the DA, the eceive choses which piece to download fom whom. Neithe UA no DA is completely accuate, but povides usually impose stonge limits on the uplink than on the downlink, which makes ou model moe ealistic.

2 nz = nz = Figue 1. Stable state in a GR stategy Figue 2. Stavation in a GR stategy A second eason fo this choice is that a sende should be able to specify which piece should be sent to which eceive, accoding to what it thinks is the best fo the collectivity (o fo its own mid-tem inteest). Specifying what is best defines an UA stategy. Convesely, a eceive mainly wishes to complete its download as quickly as possible: using moe subtle download stategies can only spoil the pee. Suppose any use able to upload at least one wanted piece will do so. This appeas to be a easonable appoximation ([1] uses a choking algoithm to stimulate the uploads), though eality is moe complex. As we show in section 4, this famewok leads to an inteesting esult, called stavation, whee unesticted upload can sometimes seveely injue the sevice capacity of a swam. When an uploade has just finished uploading a given piece, it has to choose a couple (i : pee, j : piece) and stat uploading piece j to pee i if possible. Accoding to ou UA model, a stategy is a way to choose such a pai (i, j). Fist say that a pai (i, j) is admissible fo a given pee if it possesses piece j and pee i does not. Thee exist two canonical ways to choose such a pai. Globally Random (GR) stategies consist in choosing a pai (pee, piece) at andom, like fo instance unifomly fom the admissible pais. A selective stategy consists in choosing fist a pee, then a piece, o fist a piece then a pee. Choices may be andomized1 o done accoding to some kind of (positive) discimination (aest piece fist, o emptiest pee fist). 3.2 Results 3 Simulations Ou simulations assume a constant numbe of seeds S: we place ouselves in a wost case behavio whee pees quit the swam at the vey moment they finish the download. The scenaio of a company with a fixed numbe of seves diffusing some files with the help of P2P technology would achieve this wost case. We also assume P, the numbe of pees, to be constant. We ae awae that this constitutes a ough appoximation. Indeed, defining the numbe of pees though an aival ate σ could be moe accuate and is the subject of futhe eseach. Howeve, ou esults expess bette as a function of P. Ou objective is to study how this sot of swam behaves in some natual situations. 3.1 Stategies The state of a swam at a given moment can be epesented by a boolean matix T = (tp,k )1 p P whee: 1 k K ( 1 if use p possesses the piece k tp,k = othewise Fo the sake of simplicity, let s assume eveyone has the same upload bandwidth and upload of one piece is completed in one time unit. The download/upload bandwidth atio is supposed to be infinite2, implying the numbe of pieces a pee can get in a time unit is not bounded. We choose S = 1, P = 1 and K = 1. This scenaio is motivated by the study of the flashcowd phase of a swam[8, 5], with just one oiginal seed the use that fist offeed the file to be shaed assaulted by fesh pees. Simulations using the GR stategy stating with P empty pees tend towads two diffeent stationay states, a safe state and a stavation state. Both states ae oughly equipobable with ou paametes. In safe state, all pieces ae faily distibuted among the pees, and the oiginal seed may leave without pejudice to the swam (the pees ae 1 Note that unifom GR stategy is not equivalent to bi-unifom selective stategy fo a given set of admissible couples in most cases. Fo instance, a most-wanted piece will be included in many admissible pais and be moe likely to be chosen that a common piece using unifom GR stategy. This is not the case in bi-unifom piece-then-pee selective stategy. 2 Actually, fo most people using ADSL, = 4 o = 8, but = is not unusual. Late, we will give esults fo such atios.

3 Available blocks Block Numbe Figue 3. Piece distibution in a stable state self-sufficient). In stavation state, thee exists one piece, pees ae staving fo, which most of the time nobody but the oiginal seed possesses. If the seed quits in a stavation state, the swam dies. Figue 1 shows the matix T in a typical stable state and Figue 2 shows a typical stavation state (lines epesent pees; line stands fo the seed). Selective stategies that ely on andom choices almost always convege towads stavation. If positive discimination is used (fo choosing the piece, the pee o both), a safe state is obtained. We note that all safe states ae not identical. Paametes like aveage piece density o download speed distibution can vay, as discussed in Section 5. 4 Stavation chaacteistics Stavation is a dangeous state whee the swam citically depends on the oiginal seed, hence we want to deepen the wheeabouts of this state. 4.1 Occuence The hazad of stavation in a flashcowd is intuitively easy to undestand. All safe states obseved imply all the pieces having oughly the same availability (as shown in Figue 3). On the othe hand, stavation means having a vey ae piece while the othes ae almost totally spead. Duing flashcowd, we note a geometic pogession of availability of the pieces uploaded by the seed(s) (see [11] fo a good desciption of this phenomenum). This leads to stong iegulaities of the pieces distibution in the ealie times. If those iegulaities ae not coectly smoothed by the upload stategy, the swam stavation can occu duing the ealie cycles. Theefoe andom selective stategies usually lead to stavation, wheeas positive disciminating stategies always lead to safe states: fome stategies do nothing to smooth out the pieces distibution while the latte ones cae about equity. Subsequently, we can then wonde why a safe state can be eached using GR stategy. Intuitively, the answe is that GR stategy pefoms patial positive discimination, as the pobability fo a piece k to be downloaded is basically popotional to the numbe of pees equesting it, and the pobability fo a pee p to eceive a piece is oughly popotional to the numbe of pieces it equests. 4.2 Robustness Duing stavation, we call waiting pees those having all pieces but the missing one. Because of the contaminating powe of waiting pees (assuming pees that ae able to upload do so, newcomes get the common pieces fast due to the waiting pees upload capacity, and then wait themselves), stavation can be obust even using the smatest stategy. Fo example, with a numbe of seeds S = 1 and an infinite download/upload atio, a stavation will be stable as long as the numbe of pees P is geate than o equal to the numbe of pieces K. The time to feed a waiting pee (that is one time unit if S = 1) is then geate than o equal to the time to contaminate a newcome. This esult speads fo all and S, and a sufficient (but not necessay) condition fo stavation stability, independent fom the stategy, is: P S + S(K 1)(1 + 1 ) (1) Poof A stavation is necessay stable when the contaminating powe of waiting pees is geate than the healing powe of seeds. The numbe of newcomes waiting pees can contaminate in a time unit is P K 1, whee P is the numbe of waiting pees. Seeds can heal at most S patients pe time unit. We also note that due to bandwidth atio, newcomes needs K time units to be contaminated. The healing bound implies we have (in a stavation state) P P S( K 1 + 1), that is P P S( K 1 + 1). As P long as K 1 S, that is P S(K 1), the stavation is stable (note that P can vay at each time unit). So stavation will be stable wheneve S(K 1) P S( K 1 +1). This leads to Equation (1) 3. Given the assumption that anyone able to upload a piece to somebody will do so, staving pees will always pefom good stategies to contaminate othe pees. On the othe hand, the healing stategy of seeds must be highly pecise to be efficient (each seed must heal a patient with each time unit). Thus we can say that (1) is a pecise stability bound fo stategies using positive discimination fist (whethe with espect to pees o pieces), while stavation stability in andom oiented stategies is much moe impotant. 3 Obseve that if = +, Equation (1) becomes P SK.

4 4.3 Remaks on stavation in eal netwoks Although ou model is upload-oiented, it captues a phenomenum that occus in eal pee-to-pee shaing netwoks. Fo now, we can only give intuitive easons fo that. In emule netwoks, uses tying to get a file ae waiting in a queue, and once thei tun comes, they ae ganted one (o moe) pieces. This queuing system is a pioi independent of the numbe of pieces uses possess (although thee may be a slightly negative discimination due to the fact that old pees ae moe likely to have at the same time many pieces and good positions in queues). Thus we would say emule tansfes can be seen as a selective andom stategy 4. The sensitivity of this stategy to stavation phenomena povides a possible intepetation of stavation in the case of emule. Fo BitToent netwoks, we could imagine two easons fo stavation occuence. This might happen duing the flashcowd phase if thee ae many pees eplicating almost immediately evey piece as soon as they get it, but ae set to quit the swam at the time thei download finishes (some clients can be tiggeed to do that). We think stavation can also happen when P tends towad (the flashcowd is followed by a steady, then a deceasing phase [5, 8]). If afte the deceasing phase, a piece disappeas and staving pees begin to accumulate, this may ceate a mechanical egowth of the swam in a staving state. Equation 1 shows that once a stavation occus, healing can be fastidious o even impossible. A fequent stategy fo the oiginal seed of a swam when piece availability is compomised is to e-seed, that is to eintegate the swam the time fo new seeds to appea, then to leave. The poblem is that eal staving pees may be as eage to quit as those of ou model, and may leave shotly afte thei download is complete, pepetuating the stavation. Note that some BitToent clients have an inteesting seeding mode, called Supeseed, whee the seed lies and behaves as a pee. This pevents the seed fom being polluted by equests of widely spead pieces and allows to focus on the aest pieces. This ensues a eal positive discimination stategy. Last piece impotance One may wonde whethe the existence of a piece missing is an issue. With Eo-Coecting Codes (ECC), it is possible to shae files that can be completed without all the pieces. But ECC alone can not solve the poblem fo long: knowing a missing piece is acceptable, pees will stat to behave consequently. So ECC allows a swam to function in stavation. Conside a vitual swam with K 1 pieces, what 4 In fact, some clients implements some disciminating stategies, but a significant pat does not. happens then if this vitual swam goes into stavation? If the issue of a missing piece is not managed, ECC will only delay the poblem. As a matte of fact, the missing piece may be a eal issue in P2P netwoks as they become moe impotant, and a eal optimization of the tansfes stategies can be beneficial. 5 Efficiency of upload stategies We now want to compae the diffeent stategies seen in Section 3.1, consideing QoS indicatos othe than stability, such as aveage download speed, oiginal diffusion, density, and obustness to vey geedy pees. 5.1 Linea stategy Fo the ecod, we note that ealie KaZaA potocols used to shae a file linealy (fom the fist to the last piece). If this may be advantageous fo live steaming puposes, it is not a good idea fom a stavation point of view, because the last piece will always be only possessed by seeds. Even if pees do not often quit as soon as they get thei last piece, the last pieces of the file ae vey likely to miss soone o late, unless maintaining some eliable seeds foeve. This majo dawback explains why linea stategy is no longe used in moden P2P potocols. 5.2 Aveage download speed The global download speed is bounded by the sum of upload bandwidths. Fo a (S, P) swam with unifom upload bandwidth U, the aveage download speed cannot be geate than D max = S+P P U. Simulations show that wheneve a safe state is eached, aveage download speed tends towads this limit. If the swam staves, aveage download speed can be educed: it is a good appoximation to say that only seeds can tigge the end of a download. Thus, if thee is one seed and if the theoetical minimum aveage time between 2 finished downloads is less than a time unit, pees ae going to stay idle (without uploading) pat of the time. Moe pecisely, with S seeds, the aveage download speed duing stavation is bounded by min( S.K D P max, D max ). 5.3 Diffusion duing flashcowds Flashcowd is a sensitive phase of a swam s life. If the oiginal seed leaves befoe it ends, the game is ove. Moeove, the oiginal seed often wants to minimize its upload time. Fo both easons, deployment must be fast. The minimum time fo deployment is the time fo the oiginal seed to upload each piece a time, that is K time units. This is achieved if a positive discimination on pieces is used. On

5 Aveage download speed (blocks pe cycle) 8 Aveage download speed (blocks pe cycle) Downloaded blocks numbe Downloaded blocks numbe Figue 4. Pee oiented stategy: aveage download speed in the download pogess Figue 5. Aveage download speed in the download pogess : GR stable case the othe hand, if pieces ae chosen at andom, the mean time to choose each piece at least once is equivalent to k ln(k): the buden is ln(k) times geate fo the pee compaed to positive discimination stategies. 5.4 Pieces availability In BitToent, the numbe of distibuted copies seen and the aveage download ae often consideed as good indicatos of a swam s wealth. As said in 3.2, in a safe state, each piece has oughly the same availability. Theefoe, the numbe of distibuted copies is not fa fom optimal (see Figue 3). We have also obseved that pee-oiented disciminant stategies seem to have highe piece availability fo a given P + S. Howeve, as pointed out in next paagaph, having the biggest availability is not always a good thing. 5.5 Robustness to vey geedy pees Vey geedy pees (VGP) ae pees wanting to get thei file as soon as possible and that ae likely to tick the swam to do so VGP and positive discimination Positive pee discimination helps new uses to get pieces faste. It inceases the pobability that the uploaded pieces get eplicated seveal times, as a pee with few pieces will stay longe. By constuction, this leads to stable states whee the distibution of pieces has a small standad deviation (if pooe pee is fist selected, it is close to ). Intensity of download is maximal fo newcomes, because they ae pefeed. The poblem is that the pees wait a vey long time at the end to get thei last piece, even when it is not a ae piece (see figue 4 fo download speed vesus download pogess). Thus, it is pofitable to cheat by announcing that you have to download a numbe of pieces lage than you eal one. With K = and P = 1 (paametes of figue 4), declaing 2 missing files instead of 1 inceases the aveage download speed by 86, thus inceasing the aveage effective download speed of the last piece by 43 (thee is one chance out of two to get a piece you aleady have) VGP obust stategies Let f(k) be the aveage speed download of pees possessing k pieces. A stategy is said to be obust egading VGP if asking fo pieces you aleady have does not incease you effective download speed. A andom-piece stategy is VGP-obust if f has the following popety: f(k) inceases (2) K k Poof A pee possessing k 1 pieces and declaing k 2 < k 1 pieces will have a aveage download speed of f(k 2 ) with a popotion K k1 K k 2 of useful pieces if the piece stategy is andom. Thus lying is not pofitable if f(k 1 ) > K k1 K k 2 f(k 2 ). This is the case if the function k f(k) K k inceases. We obseve that this esult holds in the case of a disciminant-piece stategy and in a safe state, because all the pieces have oughly the same density. In a staving state with seeds, this esult is false: lying allow VGPs to abuse the disciminant stategy and get the missing piece faste than it should, with heavy cost fo the swam (one of the few who possesses the missing piece leaves soone than expected). We veify easily that positive pee-discimination does not fulfill (2) fo k = K 1. On the othe hand, in GR

6 Download pogess is moe efficient than a andom stategy, so in a cetain way we could say BitToent behaves bette than edonkey fom this point of view. We have also shown that pee-oiented discimination is less impotant and can even induce bad social behavio. These esults could be used to enhance o validate existing potocols. Fo instance, a tacke awae of stavation issue could anticipate it and eseeding could be moe effective Uses (soted by download pogess) Figue 6. Distibution of download pogesses among uses in stable GR stategy stategy, the download speed (in a safe state) is basically an affine function of k (see figue 5) that fulfill (2). This lineaity can be intuitively explained if we abitay change the numbe of pieces k a given pee p possesses (all othe paametes being unchanged). The aveage speed download fo p will obviously be popotional to the K k missing pieces. Non-lineaities noted in Figue 5 come fom andom fluctuations and etoactions that have been neglected. The conclusion of the study of VGP is that positive peeoiented stategies ae not obust to lies, and that it is bette to sacifice some ove-availability and homogeneity (see Figue 6 fo a typical download distibution in GR stategy) to gain obustness, especially when that does not ham the global download speed, as we have seen. 6 Futue wok Following [9], we think it is possible to study the GR stategy stability and the pobability of staving duing flashcowds using a fluid model. This should give a base to ecommend new upload stategies. We would also like to impove ou model using heteogeneous upload bandwidth and depating and aiving of pees ([8, 5] give pecious infomation about eal distibutions). This will enhance the accuacy of ou model and will help to confim some hypothesis such as the occuence of stavation duing the decline of the swam and the utility of smat eseeding stategies such as supeseeding. Lastly, we conside analyzing logs fom edonkey seves and BitToent tackes to validate ou model. Refeences [1] B. Cohen. Incentives build obustness in bittoent, 3. [2] E. Cohen and S. Shenke. Replication stategies in unstuctued pee-to-pee netwoks. In Poceedings of SIG- COMM 2, 2. [3] F. L. Fessant and S. Patain. Mldonkey, a multi-netwok pee-to-pee file-shaing pogam. Technical Repot 4797, INRIA. [4] Z. Ge, D. R. Figueiedo, S. Jaiswal, J. Kuose, and D. Towsley. Modeling pee-pee file shaing systems. In Poceedings of INFOCOM 3, 3. [5] M. Izal, G. Uvoy-Kelle, E. Biesack, P. Felbe, A. Hama, and L. Gaces-Eice. Dissecting bittoent: Five months in a toent s lifetime. In Poceedings of the 5th Passive and Active Measuement Wokshop, 4. [6] J. Kangashaju, J. Robets, and K. Ross. Object eplication stategies in content distibution netwoks. In Poceedings of Web Caching and Content Distibution Wokshop 1 (WCW 1). [7] L. Massoulié and M. Vojnović. Coupon eplication systems. SIGMETRICS Pefom. Eval. Rev., 33(1):2 13, 5. [8] J. Pouwelse, P. Gabacki, D. Epema, and H. Sips. A measuement study of the bittoent pee-to-pee file-shaing system. Technical Repot PDS-4-7, Delft Univesity of Technology, 4. [9] D. Qiu and R. Sikant. Modeling and pefomance analysis of bittoent-like pee-to-pee netwoks. In Poceedings of SIGCOMM 4, 4. [1] I. Stoica, R. Mois, D. Kage, M. F. Kaashoek, and H. Balakishnan. Chod: A scalable pee-to-pee lookup sevice fo intenet applications. In Poceedings of SIGCOMM 1, 1. [11] X. Yang and G. de Veciana. Sevice capacity of pee to pee netwoks. In Poceedings of INFOCOM 4, 4. [12] B. Y. Zhao, J. D. Kubiatowicz, and A. D. Joseph. Tapesty: An infastuctue fo fault-toleant wide-aea location and outing. Technical Repot UCB/CSD , UC Bekeley, 1. 7 Conclusion The pape pesented an intuitive suvey of stavation issues. We showed that a piece-oiented disciminant stategy