Stay or Go?Participation in Under-Provisioned Video Streams

Dave Levin∗ Daniel Malter† Neil Spring∗ Bobby Bhattacharjee∗

University of Maryland, ∗Computer Science Department, †Robert H. Smith School of BusinessEmail: ∗{dml,nspring,bobby}@cs.umd.edu, †dmalter@rhsmith.umd.edu

ABSTRACTWe consider the problem of choosing whether or not to par-ticipate in a video streaming session under the condition thatthere is insufficient upload capacity to serve all peers. Weexplore the connections between this problem and that ofmarket entry. The fundamental difference arises from a lackof a centralized coordinator. In end-system multicast, peers’decisions must be based on local policy and observations.We find that careful selection of local policy—specifically,the pairwise trading policy among peers—assists in not onlyfinding the equilibrium of market entry, but can also improvethe equilibrium by increasing the number of entrants.

1. INTRODUCTIONVideo streaming services, such as youtube.com and

hulu.com, have become immensely popular in recentyears. Their ability to scale to this demand is largelybased on highly provisioned, centralized servers, whichcan be extremely expensive. Peer-to-peer video stream-ing offers a less expensive alternative, without requiringextensive pre-existing infrastructure or server capacity.Rather, the peers viewing the stream would be largelyresponsible for providing the stream.

While the common assumption is that each peer isable to give to the system as much as she requests fromthe system, this assumption may not hold in practice.In this paper, we study the problem of streaming videoto a set of peers who collectively do not have enoughupload capacity to allow all of them to view the stream.

The fundamental goal in this space is for there to beas many peers in the system as can be supported. Webegin by looking at the problem of an under-provisionedsystem in a centralized setting (§2), and demonstratesimilarities to market entry. This parallel lends insighttoward an algorithm we present for determining themaximal subset of participants who can take part ina video streaming system.

We then turn to a decentralized setting, providingan algorithm for determining when a peer should leavea system they determine to be under-provisioned (§3),and studying what effect local trading policy has on theglobal system-wide properties (§4). The central hypoth-esis to this work is that local (decentralized) tradingpolicies are sufficient for obtaining high levels of partic-

p1

p2

p3R

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c1

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Figure 1: (a) Sample topology with stream rateS. Peer pi has capacity ci. (b) The server kicksout p3 so that (c) more peers can join.

ipation. We test this hypothesis via simulations (§5) oftwo allocation mechanisms: BitTorrent’s unchoking al-gorithm [2], and the proportional share allocation mech-anism [3].

2. OPTIMAL, CENTRALIZED SOLUTIONSWe begin our study of participation in an under-

provisioned system by first assuming a centralized coor-dinator. We demonstrate parallels between participat-ing in a peer-to-peer system and market entry. Buildingoff of classical market entry results, we sketch an opti-mal solution in this simplified setting.

2.1 A centralized system designConsider the following strawman setting: new peers

register with a centralized topology server, providingtheir IP address and port (so future peers can contactthem), as well as the amount of capacity they are willingand able to provide to the system. The role of thecentralized topology server would be to determine if anew user may join the system, and if so, to computethe topology that incorporates that user. We expectthat the goals of such a service would be to optimizethe number of participants in the stream, as well as theavailability for the participating peers.

Deciding which peers can stay in the system can beviewed as an online scheduling problem. Consider the

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example in Figure 1. Peers p1 and p2 both have thecapacity of the stream rate, while other peers have lessthan the stream rate. Initially, in Figure 1(a), p3 gainsfrom the system without giving anything in return. Fur-ther, no peer with upload capacity less than 0.9S couldobtain the stream rate without p3 leaving the system.

As peers request to join the system, the centralizedtopology server would have to decide whether or notto let them enter. This decision can involve removingexisting participants from the system. When peer p4 re-quests to join the system in Figure 1(b), the server mustdecide whether or not to allow p3 to stay. Keeping p3

provides greater uptime to the participants. However,because p4 offers greater upload capacity than p3, al-lowing p4 to join increases the number of peers whomay join in the future. In the above example, p3 loseshis position in the swarm to p4. As a result, p5 in Fig-ure 1(c) is able to obtain the stream; along with p4, shecan provide enough capacity to allow for four peers.

A challenge in this basic, centralized approach is inobtaining truthful capacity information from joining peers.In the example in Figure 1(a,b), for instance, how doesthe server know c3 < c4 if the peers do not need to up-load to anyone? There are several potential solutionsto this, such as uploading garbage data, as in BAR gos-sip [4], but this places strain on the topology server asmany new peers join.

2.2 Participation as market entryThe question is thus how to design a protocol in which

peers’ donations are distributed in a way that assurescontinuing participation and efficiency as well as thedistribution of the good among as many participants aspossible. We derive an intuition for how we can solvethis problem from the literature on market-entry games.Even though the setting of a market entry game is dif-ferent, the logic behind the allocation we propose is verysimilar.

In the simplest case of a market entry game, a numberof competitors n decides whether to enter or stay outof a market with fixed capacity c, where n > c. Let thepayoff from entering the market be πi = c−

∑i ei, where

ei is a binary indicator that takes 1 if actor i decides toenter the market. Assume for simplicity that the payofffrom staying out of the market is 0. When the numberof entrants into the market is greater than market ca-pacity, the market is over-utilized and all entrants incura loss. On the other hand, if too few competitors enterthe market, the market is underutilized and all entrantsincur a profit. The market is thus in equilibrium if thereare as many entrants as there is market capacity.

This special, symmetric case of a market entry gamecan be generalized. Selten and Guth [8] derive theoret-ical propositions for equilibrium point selection whenentering the market is costly and when costs are asym-metric. When the potential costs of entering the market

are ordered among the competitors, then the equilib-rium point selects market entrants by the order of theentry costs. In other words, the competitors with lowentry costs enter the market to the point where the mar-ket is used to efficiency, whereas the competitors withhigher entry costs stay out.

This equilibrium point selection has, in our view, im-portant, natural implications for the design of partici-patory systems. Accepting into a system the peers whoincur lower marginal cost appears to be a natural designprinciple. In the remainder of this section, we use thisdesign principle as a basis for an optimal, centralizedalgorithm. We then use this optimal allocation as thebaseline for comparing the decentralized protocols thatwe present in §4.

2.3 Finding the maximal participantsThe market entry game’s Nash equilibrium provides

a template for determining the maximal number of par-ticipants in a video streaming system. We begin withthe following observation:

Observation 1. If a video streaming system consistsof k peers, each of these peers can obtain the stream rateonly if the sum upload capacity is at least (k − 1)S.

Ahlswede et al [1] proved that, with network coding,this condition is not only necessary but sufficient. Usingthis result, we can now answer: what is the maximalsubset of peers who can obtain the video stream?

We present in Algorithm 1 a method for comput-ing the maximal set of participants given their uploadcapacities. This algorithm parallels the market entryNash equilibrium; peers are sorted by their upload ca-pacities, and included in the system one by one untilsystem capacity is reached.

Algorithm 1 Maximal participation determinationPeers pi has upload capacity ci, i = 1, . . . , N .

1. Sort {ci}i=1,...,N in decreasing order. Supposec1 ≥ c2 ≥ · · · ≥ cN .

2. for i = 1, . . . , N :

(a) If adding pi to the set of participants woulddecrease the sum capacity to less than (i−1)S,then return; add no more participants to thesystem.

(b) Otherwise, add pi to the set of participants.

We believe that this algorithm can be extended to find-ing the topology by which to achieve the stream ratefor all permitted participants, but investigating suchtopologies is beyond the scope of this paper.

Although Algorithm 1 finds the maximal number ofparticipants, it does not impose any fairness constraints.

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We return to this point in the context of the decentral-ized strategies that we consider in the remainder of thepaper. Determining the maximal set of participantswho can be arranged in such a way as to ensure re-silience to free-riding is an area of future work.

3. WHEN TO LEAVE?In the remainder of this paper, we consider only de-

centralized solutions. The first difficulty in moving awayfrom a solution by fiat is in determining who can par-ticipate in the network; there is no centralized coordi-nator with perfect information who can inform a peerwhether or not they will be able to view the videostream. Rather, peers must determine via their ownlocal observations whether or not they are able to viewthe stream.

3.1 A priori information is not enoughNot all peers can base their decisions of whether or

not to join the system on their upload capacity alone.Figure 1 demonstrates this; p3 was able to join the sys-tem in configuration (a), but would not be able to joinin configuration (c). Certainly, it should hold that peerswith upload capacity no less than the stream rate canobtain the stream rate from the system. However, theremay not be a clear cut-off capacity, such that any peerwith at least this capacity can be guaranteed to obtainthe stream rate.

3.2 Waiting for others to leave firstPeers must enter the system in order to determine if

they have sufficient capacity to gain from it. This in-troduces a challenge not present in classic market entrygames: peers must decide not only whether to leave thesystem, but when to leave the system. Certainly, a peermust remain in the system long enough to get an ac-curate measure of what her steady-state download ratewould be. A peer also has incentive to stay in the sys-tem in the hopes that others will leave, thereby freeingup capacity for her.

We focus on this problem of avoiding mass, unnec-essary departure from the system. Just as 802.11 at-tempts to avoid multiple hosts sending at the same time,we attempt to avoid too many hosts leaving the streamat the same time. Suppose a new peer were to join thevideo streaming system in Figure 1(c) such that one,but not both, of p4 and p5 would have to leave. Asboth peers are affected by the new peer’s entry, theymay both begin obtaining less than the stream rate atthe same time. A deterministic protocol for leaving—for instance, leaving after not obtaining the stream forsome fixed F rounds—would result in both p4 and p5

leaving at the same time. The same effect is prevalentalso when multiple peers join at the same time.

We present in Algorithm 2 a randomized protocol forselecting when to depart a system. Our intuition is that

peers who are “close” to obtaining the stream rate havegreater expectation to receive it if other peers leave, andtherefore stay in the system with greater probability.

Algorithm 2 System departure.If p has not obtained the stream rate (and this algorithmhas not been called) in the previous F rounds, leavewith probability

1 − Average received in the last F roundsStream rate

(1)

We considered also incorporating a peer’s capacityin their decision to leave, the goal being for higher-capacity peers to wait longer before leaving. However,this presupposes knowledge of a distribution of capac-ities; to be properly formulated, a peer would have totake into account the expected number of peers whohave greater capacity than she. For example, a peermay expect that she has very low capacity, when, incomparison, she has the greatest capacity amongst allpeers not yet obtaining the stream rate. We expectthat download rates are a more accurate indicator of apeer’s relative contribution to the system, and limit ouralgorithm to incorporate only this.

4. LOCAL TRADING STRATEGIESOur hypothesis is that global, system-wide optimiza-

tions can be obtained by local, selfish strategies. In thissection, we review two local strategies that have re-ceived attention within the context of the BitTorrentfile swarming system [2]. We discuss how well we ex-pect them to apply in an under-provisioned multicastsystem, and evaluate them experimentally in Section 5.

We assume a mesh-based system, wherein peers con-nect to a random set of neighbors, some of which may bethe streaming server(s). Mesh-based streaming systemshave received attention as a more resilient alternative totree-based systems, although trees are typically more ef-ficient. We believe that mesh-based streaming systemsoffer greater flexibility in peers’ local policies; peers ina mesh have more freedom in terms of with whom andhow much they trade, while a tree by definition imposesa more rigid topology.

4.1 BitTorrent unchokerBitTorrent [2] is a decentralized file swarming system

that breaks a large file into pieces, and establishes amesh of peers who trade these pieces with one another.There have been various studies into using BitTorrentas a video streaming system [5–7]. We do not considerthe broader systems design issues in this paper, andfocus only on the local allocation policy, referred to asBitTorrent’s unchoking algorithm.

We present BitTorrent’s unchoking algorithm in Al-gorithm 3. BitTorrent peers reward their top k (typ-

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ically 4) contributors, as well as one peer at random,with equal shares bandwidth.

Algorithm 3 BitTorrent’s unchoking algorithm.Run at peer p, with capacity cp, at round t:

1. In round t− 1, peer qi uploaded bpi (t− 1) to p, for

i = 1, . . . , N .

2. If qi was one of the top k contributors from theprior round, bi

p(t) = cp/(k + 1).

3. Choose another peer qo at random and optimisti-cally unchoke: bo

p(t) = cp/(k + 1).

Unfortunately, the mechanism to allocate the receiver’sresources to a limited number of donors by an equalsharing rule has obvious design flaws that can result inan inefficient set of system entrants. Assume a closedsystem of six participants in a network and considera receiver who requires resources of 1 to obtain thevideo stream. Suppose the receiver obtains contribu-tions from five donors (say, 0.30, 0.25, 0.20, 0.15, 0.1).With BitTorrent’s unchoker, the fifth donor (0.1) willnot be rewarded by the receiver. The fifth donor hasthus the following strategies at hand: (1) exit and donot contribute to the receiver in the next round, (2) in-crease the contribution to the receiver to end up amongthe first four places (i.e. place a higher bid), or (3) keepthe bid constant or even reduce the bid in the hopethat one of the current bidders with a higher bid ceasesdonating to this receiver. Obviously, the first strategyposes a serious threat to the system. If the fifth donorstops donating to the focal receiver, the receiver will beunable to procure the good because the sum of the do-nations to him amounts to only 0.9. It is easily conceiv-able that such a system can fail when resources amongparticipants are scarce and asymmetrically distributedso that some network participants are net contributors,whereas other network participants are net receivers.

4.2 Proportional share allocationThe proportional share auction has recently received

attention in the context of file swarming [3, 9]. It istrivially fair, and has been demonstrated to be resilientto a wide range of strategic attacks [3]. We present itin Algorithm 4.

Algorithm 4 Proportional share unchoking algorithm.Run at peer p, with capacity cp, at round t:

1. In round t− 1, peer qi uploaded bpi (t− 1) to p, for

i = 1, . . . , N .

2. bip(t) = cp · bp

i (t − 1)/∑

j bpj (t − 1)

In addition to providing greater resilience to selfish

participants [3], we expect that proportional share canyield high levels of participation, for two main reasons.

First, with proportional share, the more a peer gives,the more that peer gets. This fairness property does notnecessarily ensure that a peer will get as much as shegives. However, it exhibits similar behavior to the max-imal participant algorithm (Alg. 1); via proportionalshare, peers with greater capacity stand to gain moreof the stream rate. Further, with proportional share,peers have incentive to give as much of their capacityas is necessary to obtain the stream rate.

Second, proportional share yields a clear signal ofwhether a peer will be able to obtain the stream rate ornot. BitTorrent’s 1/4-or-nothing unchoking algorithmmakes it more difficult to anticipate how much a neigh-bor may give in future rounds. Conversely, proportionalshare is more continuous by nature, allowing a peerto more accurately detect a decrease in contributionfrom a neighbor. As such, we expect that low-capacitypeers will realize quickly and clearly that they are un-able to obtain the stream rate, while higher-capacitypeers can observe when they are close to the streamrate, and therefore out-wait other peers, according toAlgorithm 2.

5. SIMULATION STUDYWe study via simulation whether local allocation pol-

icy can yield market efficiency in under-provisioned set-tings. We compare the equilibria of the two local poli-cies presented in §4 to the desirable outcomes discussedin §2.

5.1 Simulation detailsIn our simulation, all peers join at the same time, and

are provided an initial contribution level for every otherpeer. Peers then run either a BitTorrent-like top-fourallocation, or a proportional share allocation mecha-nism. We do not consider mixes of clients; in a givenrun, all peers run the same allocation mechanism. Peerschoose to leave the system according to Algorithm 2,waiting for 10 rounds before probabilistically choosingwhether to leave.

The primary goal of our simulations is to determineunder what conditions of upload capacities a given local-policy-based allocation mechanism achieves high levelsof participation. Of course, the set of feasible partici-pants in a system depends on the system-wide distribu-tion of upload capacities. Thus, peers in our simulationshave different upload capacities, and the fundamentalindependent variable is the distribution of upload ca-pacities.

5.2 Who stays and who goes?We first study who is allowed entry into the system

under varying allocation strategies. To understand this,we plot the inter-peer allocations at equilibrium for Bit-

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0

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Figure 2: Clustering within a stream of top-4 clients.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

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Figure 3: Clustering within a stream of proportional share clients.

Torrent’s top-four (Figure 2) and proportional share(Figure 3). In these figures, a point at (x, y) denoteshow much a peer with capacity x donated to a peerwith capacity y, the amount of which is represented bythe intensity of the shading. Peers who neither receivenor download in these figures have left the system.

With proportional share, all peers with capacity greaterthan or equal to the stream rate obtain the stream rate.Additionally, there are some peers with capacity lessthan the stream rate who also are able to remain in thesystem. As demonstrated in the series of plots in Fig-ure 2, the number of lower-capacity peers who obtainthe stream rate increases with excess market capacity.Further, these figures show that there is not a clear“cut-off capacity” that distinguishes between peers whomay and may not obtain the stream. Rather, for low-capacity peers (who require extensive market excess), itis their random set of neighbors and initial contributionlevels that determine whether or not they are able toobtain the stream.

BitTorrent’s top-four unchoking algorithm does notyield as favorable results. While peers with greater ca-pacity are more likely to obtain the stream rate, no peerappears to be guaranteed access to the system. Rather,there are peers with significantly more capacity thanthe stream rate who do not obtain the stream, as wellas peers with considerably less capacity who do obtainthe stream.

5.3 Comparison with maximal participantsWe next study how close to the maximal number of

participants these two local allocation algorithms areable to obtain. Recall that the number of peers able toenter the system increases with greater excess market

0

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Rat

io o

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PT

Average upload capacity (Frac. of stream rate)

PropShareTop-4

Figure 4: Number of system participants com-pared to the maximal amount from Algorithm 1.

capacity. We therefore plot in Figure 4 the fraction ofthe maximal participants (as computed by Algorithm 1)with varying average system-wide capacity.

Proportional share obtains nearly the maximal num-ber of participants when the average system-wide ca-pacity is 25% greater than the stream rate. The Bit-Torrent unchoking algorithm requires more than doublethis amount of capacity to obtain the same fraction ofthe maximal amount. This result demonstrates the ex-tent to which the choice of a local allocation mechanismcan affect the global properties of system participation.

5.4 When do peers leave?We close our evaluation study by investigating when

peers leave the system. As indicated in §3, low-capacity

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Peer departureMin. entry capacity

Figure 5: Order of departure from a stream ofBitTorrent clients. Average capacity is 0.75

peers would leave first, allowing higher-capacity peersthe opportunity to benefit from excess market capacity,while providing more to the system in return. We plotwhich peers leave, identified by their upload capacity,over the course of a simulation run for both BitTorrent(Fig. 5) and proportional share (Fig. 6) clients. Bothclients use Algorithm 2 to determine if and when toleave.

Note first the distribution of the dots in Figs. 5 and6. As in our other results, no proportional share clientswith capacity greater than the stream rate leave thesystem. For both clients, the majority of low-capacitypeers leave first, and higher-capacity peers typicallyleave later. This is particularly evident in the case ofthe BitTorrent client, perhaps due to the fact that thereare more high-capacity peers leaving the system.

The lines in Figures 5 and 6 represent the minimalcapacity necessary to participate in the system, as de-termined by Algorithm 1. Recall that this algorithmsorts the remaining peers in the system and adds themto the maximal participation set until the system is sat-urated. We run this algorithm every time a peer leavesthe system, and plot the capacity of the last peer addedto the maximal participation set. We emphasize thatwe determined the maximal participants only to calcu-late this capacity value; it did not affect the simulatedbehavior in any way.

Ideally, no peers above this line would ever leavethe system, and all peers with capacity below this linewould; this would precisely yield the maximal alloca-tion. In other words, departures below the line are de-sirable for achieving a large number of system partici-pants, while departures above the line are undesirable.

With these minimal capacities in mind, a comparisonbetween the proportional share and BitTorrent clientsbecomes clearer. Few proportional share peers abovethe minimal capacity line leave after a short period of

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Peer departureMin. entry capacity

Figure 6: Order of exit from a PropSharestream. Average capacity is 0.75.

time, while the vast majority of BitTorrent departuresare of peers who ought not have needed to leave.

6. CONCLUSIONWe have considered the problem of determining the

optimal number of participants in an under-provisionedsystem. In the centralized setting, we demonstratedparallels to the problem of market entry, which lentinsight into the formulation of an algorithm for deter-mining the maximal participation set. In the contextof decentralized systems, proposed the hypothesis thatlocal-policy allocation mechanisms can achieve greateramounts of participation. Our simulation evaluationsupports this hypothesis, and demonstrates that thechoice of an allocation mechanism can have significanteffect on the resulting number of viable participants.

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