Effective Utilization of User Resources in PA-VoD Systems with Channel Heterogeneity

Transcription

1 1 Effective Utilization of User Resources in PA-VoD Systems with Channel Heterogeneity Le Chang, Jianping Pan, Senior Member IEEE, and Min Xing Abstract Nowadays, peer-assisted video on-demand (PA-VoD) systems offer high-definition (HD) channels to online users. However, the quality of service in such HD channels is usually not comparable to the standard-definition (SD) ones, as HD channels have to seek more bandwidth support and cache space from peers, which is a challenging task. In this paper, we focus on peer cache and upload bandwidth management at the same time for multi-channel PA-VoD systems with heterogeneous video playback rates, i.e., HD and SD channels coexist with different bandwidth and cache requirements. We first take user viewing behaviors into account and derive the statistical performance bounds on server bandwidth consumption, which lead to the conclusion that such behaviors can easily affect the provisioning for HD channels, even if there is enough upload bandwidth from SD peers. We then formulate bandwidth allocation as a linear programming problem to calculate the tight lower bound at any time instant, with global information available and system-wide coordination possible (e.g., through a tracker). Next, we design heuristic algorithms for peer cache replacement and upload bandwidth allocation to fit with the nature of a P2P structure, and the results are compared with the statistical and instance performance bounds through extensive simulation, which shows the efficacy of the proposed algorithms in dynamic scenarios. Index Terms Peer-to-peer video streaming, video on-demand, bandwidth allocation, caching strategy, view-upload decoupling I. INTRODUCTION Nowadays, peer-assisted video-on-demand (PA-VoD) systems have demonstrated a great potential to harness the vast amount of peer-contributed resources, such as peer upload bandwidth and cached content, to lower the server bandwidth consumption [1]. By the virtue of peer contribution, these systems are capable of providing large-scale multi-channel VoD services, while keeping the maintenance cost low. However, due to the heterogeneity of the channel playback rate and popularity, as well as dynamic user behaviors, the bandwidth supply from peers varies greatly between channels, which poses the grand resource imbalance challenge to the research community. According to PPLive, small channels with low population often suffer from poor performance as a result of the limited bandwidth supply from participating peers, while popular channels may have extra upload bandwidth left[2]. The bandwidth deficit in high-definition(hd) channels is also widely observed in PPLive and UUSee [3], [4], as a result of the bandwidth demand for HD channels greatly exceeding the average peer upload capacity. L. Chang, and J. Pan are with the Department of Computer Science, University of Victoria, Victoria, BC, Canada( {lechang, pan}@uvic.ca); M. Xing is with the Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada ( mxing@ece.uvic.ca). To overcome the bandwidth imbalance problem in peerassisted live streaming systems, the view-upload decoupling (VUD) strategy was proposed, which decouples what a peer is uploading from what it is watching, and tries to equalize the global bandwidth demand-to-supply ratio for every channel, i.e., a water-leveling approach [5], [6]. However, in PA-VoD systems, such a problem calls for a more delicate solution involving two major components: bandwidth allocation and cache management, as peers watch and cache different parts of a variety of video programs. Therefore, the objective is to design an appropriate coordination of these two components, such that the supply for each part of each video program meets its demand by peer-contributed resources as much as possible. This not only offers a better user experience, but also reduces the bandwidth consumption and maintenance cost at the server, as ISPs charge VoD service providers based on the 95% consumed bandwidth or the total data volume [7]. Water-leveling approaches for PA-VoD systems have been studied at the movie level with homogeneous, moderate playback rate [8] [11]. However, HD movies need much more bandwidth supply and cache space, and the content may not be completely cached at peers, which makes the existing approaches inapplicable. Water-leveling may also apply to the segment level [12], [13], but obtaining the demand-to-supply ratio for each segment in real time is a major challenge. In this paper, we aim at solving the resource imbalance problem in PA-VoD systems with the channel playback rate heterogeneity and dynamic user behaviors. We take two constraints of the problem into account: 1) each peer has a limited cache size; 2) the playback rate of some channels in the system exceeds the average peer upload capacity, e.g., HD channels. We allocate and balance two kinds of resources, peer cache and upload bandwidth, under different user viewing behaviors. To the best of our knowledge, this is the first analysis and performance evaluation work of PA-VoD systems explicitly accommodating HD channels and different user behaviors. Our contributions in this paper are highlighted as follows. We build a queuing network model at the movie level to derive statistical performance bounds for PA-VoD systems with heterogeneous playback rates and dynamic user behaviors. The model indicates that user viewing behaviors can largely affect the bandwidth provisioning for HD channels, e.g., switching to SD channels after watching HD movies is highly desirable to reduce server bandwidth consumption. In addition, a tractable linear programming optimization problem is formulated at the segment level to minimize the server bandwidth consumption for any given instance of the system at any time. It provides tight instantaneous performance bounds, and thus serves as

2 TABLE I: Important Notations Symbol Definition SBC The total server bandwidth consumption D, B The total bandwidth demand/supply of peers η The efficiency of utilizing the peer upload bandwidth r S, r H The playback rate of an SD/HD movie T The time duration of each movie S The number of distinct segments in the system P c, P m The transfer probability matrix between all available video categories/channels p c ij, pm ij The probability of transfer from category/movie i to j ū p The average upload capacity of all peers u j The upload capacity of peer j N The number of peers in the system N S, N H The expected number of viewers in SD/HD channels in the steady state N i, H i The expected number of viewers/helpers of channel i in the steady state W The watching matrix that indicates which peer is watching which segment C The cached matrix that indicates which peer has cached which segment A The allocation matrix that indicates a bandwidth allocation the perfect benchmark when evaluating bandwidth allocation algorithms. We also develop heuristic bandwidth allocation and cache management algorithms without calculating the dynamic segment-level demand-to-supply ratio. The performance is evaluated with comparison to the segment-level waterleveling strategy and our lower bounds through extensive simulation, which verifies the efficacy of our algorithms in dynamic scenarios. The remainder of this paper is organized as follows. In Section II we build mathematical models to capture the steadystate and transient behaviors of PA-VoD systems, where three analytical bounds are obtained. Heuristic algorithms are proposed in Section III, which are then evaluated in Section IV. We review the most related work in Section V. Section VI discusses the further work with conclusions. II. SYSTEM MODEL In this section, we build analytical models to capture the major characteristics of PA-VoD systems and user behaviors. We first describe the settings and assumptions of our models, and then present theoretical bounds for the server bandwidth consumption in the steady state and at any time instance. The terms and notations that we often use in this paper are listed and briefly explained in Table I. A. Model Description and Assumptions We assume all video programs (movies) are released from a central server (or servers), and the server is able to support any peers at any time. However, the amount of such server-offered bandwidth will add up to the server bandwidth consumption, SBC. There are two categories of video programs, standarddefinition (SD) and high-definition (HD) movies, and peers watching SD (HD) movies are referred to as SD (HD) viewers. The playback rate of HD movies r H is much higher than the average peer upload capacity ū p and that of SD movies r S lower than ū p, which are quite representative in today s multichannel VoD systems [3], [4]. We adopt the well-accepted assumption that there is no downlink bottleneck, since the peer download capacity (1.5 Mbps for typical DSL connections) is usually large enough to accommodate HD videos. Another common assumption is that each peer contributes a finite cache space which can only store a small number of movies [8], [1], [11]. Taking into account the fact that HD movies usually occupy more cache space, we assume the peer cache can store either two complete SD movies or a single HD movie, and all movies are assumed to have the same time duration, T. This is reflected by the typical settings of real systems. For example, the size of the local cache is fixed at 1 GB in PPLive [2] and PPStream. For an SD (HD) movie of playback rate 5 (1,) Kbps, the cache can store about two SD movies or one HD movie, each of 2.3 hours, a representative time duration of full-length movies. We further divide an SD (HD) movie into 1 (2) segments to facilitate the segment-level optimization. Here the segment is the unit for content scheduling, and all segments have the same size, i.e., 1/2 GB for a 1-GB peer cache, which is comparable to the settings in real systems [3]. To ensure that a user watches a movie smoothly, the user download rate must catch up with the video playback rate. In this paper, we assume that peers stream exactly at the video playback rate, which is also a common assumption in [1], [12], [14] [16]. Peers first attempt to seek bandwidth supplies from each other, and resort to the server at last if the desired streaming rate still cannot be achieved. In multi-channel VoD systems, it is possible that a peer is uploading the content of a channel other than the one it is watching. Such peer is referred to as a helper of that channel [12], [13]. There are N peers in the system. When watching a movie, a peer starts from the beginning of the movie and watches each segment sequentially until finishing the last one. After that, the peer will transfer to another channel. Such user behaviors follow the stationary model proposed in [5], [6], [8] [1]. Although the stationary model does not capture the evolution of movie popularity and peer churning in real systems, it resembles the scenarios of a short duration (usually several hours) when the population of online peers is stable, and insights gained from the model can facilitate understanding more dynamic scenarios. When transferring to another channel, we assume a peer first determines whether it will stay in the same movie category (i.e., SD or HD). A transfer matrix P c at the category level is used to capture this behavior, with elements p c ij defined as the probability of transferring from category i to j. For instance, p c HS denotes the transfer probability from HD to SD movies. After determining the next category, a peer selects a movie in the chosen video category to watch. The transfer between any two movies is determined by a transfer matrix P m at the movie level, which conforms to P c. Considering that a user usually does not return to the movie it has just watched, we set p m ij =, if i = j. Therefore, such user transfer behaviors at the category and movie level can be simply modeled as Markov Chains. B. Movie-Level Steady-State Analysis In this section, we present the steady-state analysis at the movie level, when the transfer matrix P c and P m are given, i.e., the user behavior is known. The server bandwidth 2

3 Fig. 1: The queuing model for a single HD channel with FIFO cache replacement consumption (SBC) can be simply computed as the total bandwidth deficit of peers, i.e., SBC = (D Bη) +, where D is the total bandwidth demand, B = Nū p is the total upload capacity of all peers, a + := max{a,}, and η 1 is the bandwidth efficiency factor, which indicates the efficiency of utilizing the peer upload bandwidth. From the transition probabilities in P c and P m, we can derive the expected performance in the steady state, such as N S (N H ) as the expected number of peers watching SD (HD) movies, and N i as that of each movie i, etc. Therefore, the expected total bandwidth demand is D = N S r S +N H r H = N( pc HS rs p + pc c SH rh HS +pc SH p ). According c HS +pc SH to our model, there exists the case that a peer happens to watch an SD movie i already stored in its local cache, when the movie it is currently watching is the one that it watched 2T ago. The probability can be calculated as P null = i {SD} (pm p m j pm ji p m i pm ij i j {SD} ), k {SD} pm k pm ki k {SD} pm k pm kj where p m i is the steady-state popularity of movie i, which can be computed from the transfer matrix P m at the movie level. Considering such no demand peers, the sever bandwidth consumption can be calculated as SBC = (D Nr S P null Bη) +. (1) Setting η = 1, which means that all peers are able to fully utilize their upload bandwidth to support others, we have the first performance bound, Bound I, for the server bandwidth consumption. Due to the limited cache size of each peer, a peer cannot always find the needed video content from other peers. In this case, the peer upload capacity is underutilized, which is referred to as content bottleneck. This will lead to η < 1, so the goal of the system is to maximize η. In our system, SD viewers have more upload bandwidth than their demand (ū p > r S ), which can be allocated to help HD viewers. However, the amount of such bandwidth is determined by the availability of HD content cached by these SD viewers. We can develop a group of bandwidth allocation strategies following the Bandwidth Helping Principles: viewers in the same SD channel first try to satisfy their own bandwidth demand within the channel, and then use the extra bandwidth to upload the cached content, if needed, to HD viewers. HD viewers will never serve as helpers for other channels as they have already suffered from their own bandwidth deficit. To derive the maximum bandwidth efficiency η for bandwidth allocation algorithms following the Bandwidth Helping Principles, we start from a single HD channel, and build a simple queuing network to obtain the expected number of viewers and helpers when a FIFO cache replacement strategy is adopted by each peer, which is shown in Fig. 1. Let x i (t) denote the number of viewers in an HD channel i at time t. After a peer finishes watching the HD movie, it has the HD content in its cache, which will remain for a while. When the peer transfers to another HD channel after watching channel i, it cannot serve as a helper and will leave the queuing system immediately, with probability p c HH or pc SH. If it has not transferred twice to SD channels yet, the cached HD content still remains, and this peer is considered as a helper for channel i. Therefore, we let y i (t) and y i (t) denote the number of helpers for these two cases: peers that are watching the first and the second SD movie after finishing movie i. These viewers and helpers form a queuing network including three G/D/ queues with service time T. In the steady state, the arrival rate of each viewer and helper to any queue equals the corresponding departure rate, and the time index t is omitted. Therefore, λ i = x i /T, x i /T p c HS = y i/t, y i /T p c SS = y i /T, and x i = N i. Solving the equation set above, the total number of helpers for channel i is H i = y i +y i = N i(p c HS +pc HS pc SS ). From the equation above we can see that in the steady state, the number of helpers for each HD channel is in proportion to the viewers in that channel. Moreover, if the expected numbers of HD and SD viewers N H and N S are fixed (i.e., Bound I is fixed), we can derive p c SS = 1 pc SH = 1 pc HS N H/N S, so H i = N i p c HS (2 pc HS N H/N S ), which is monotonously increasing on p c HS [,1], if N S > N H. That means, if there are more SD viewers than HD ones, which is usually the case in real systems [3], transferring to SD channels after watching an HD movie (a larger p c HS ) will bring more helpers for the HD channel (a larger H i ). With H i derived, the supply that can be offered by such helpers is (ū p r S )H i and the total amount of such helping bandwidth in the system is i {HD} H i(ū p r S ) = N H (p c HS +pc HS pc SS )(ū p r S ). Also let the bandwidth of the no demand SD viewers be equally utilized by other SD viewers, and such helping bandwidth is increasedto N H (p c HS +pc HS pc SS )(ū pn S /(N S NP null ) r S ). Therefore, the maximum bandwidth that can be utilized from peers is B max = (N S NP null )r S + N H ū p + N H (p c HS + p c HS pc SS )(ū pn S /(N S NP null ) r S ), and the maximum bandwidth efficiency is thus η max = B max /Nū p. Taking η max into Eqn. (1), we have Bound II, where the content bottleneck is considered. C. ment-level Transient-State Analysis Although the steady-state analysis offers statistical bounds, a PA-VoD system can be highly dynamic, which makes the system performance deviate from these expected bounds at any given time. To understand transient-state behaviors of PA- VoD systems, we continue to study the optimal bandwidth allocation at the segment level at a given time instant, by assuming that all needed global knowledge is known. We define three S N matrices, where N is the number of peers and S the total number of distinct movie segments in the system at a given time. The S movie segments are grouped by different movies, and listed in the sequential order 3

4 for each movie. The watching matrix W represents which peer is watching which movie segment, with the elements w ij = 1 if peer j is watching segment i, and w ij = otherwise. The cached matrix C characterizes the cached content of each peer, where c ij = 1 if peer j has segment i, and c ij = if not. An allocation matrix A contains the solutions, with the elements a ij 1. a ij represents the percentage of the upload bandwidth that peer j allocates to movie segment i, and a ij u j is the amount of such bandwidth allocated, where u j is the upload capacity of peer j. We assume all such global information (W, C) is known for now in this section. The bandwidth demand for a movie segment i is composed of the required streaming rate of all peers watching it, if the peer does not have the segment in its local cache, which can N be computed as D i = r i j=1 (w ij c ij ) +, where r i is the playback rate of segment i. The supply B i is computed as B i = N j=1 a iju j. Similar to Eqn. (1), we have SBC = S i=1 (D i B i ) +. However, such an objective function for SBC exhibits a nonlinear programming problem, which is very hard to solve. Therefore, we convert the formulation into a tractable problem by introducing a new S 1 vector U s, with the element u s i defined as the amount of bandwidth allocated to movie segment i from the server, and the objective function is converted to minimizing the total server bandwidth consumption S i=1 us i, with the constraint that the demand of each segment is equal to the supply from the server and other peers. Another constraint is that a peer cannot be assigned to upload any movie segments that it does not have in its local cache, i.e., i,j, a ij =, if c ij =. Moreover, for each peer, the sum of such bandwidth allocation percentages should be S less than or equal to 1, i.e., j, i a ij 1. The problem can then be formulated as Min S i=1 u s i s.t. i,j, a ij =, if c ij = ; i, u s i ; S i,j, a ij 1 ; j, a ij 1; i, N N u j a ij +u s i = r i (w ij c ij ) +, (2) j=1 i j=1 with all a ij and u s i as the unknown variables. Now the formulation exhibits a linear programming problem and thus is solvable in polynomial time in a centralized manner. Although the optimization solutions are difficult to obtain for largescale systems in real time, they do provide guaranteed performance bounds for different scenarios, which we refer to as Instance Bound or Bound III. Moreover, as the optimization is independent from any bandwidth allocation algorithms, we expect that such a solution will lead to a server bandwidth consumption even lower than Bound II, which will be verified in Section IV. Finally, we summarize the three bounds we have derived in this section. Bound I gives the best expected server bandwidth consumption by assuming that all upload bandwidth from peers is fully utilized, and thus there is absolutely no content bottleneck. Bound II takes the content bottleneck into account, where the bandwidth allocation follows the Bandwidth Helping Principles and the cache replacement follows FIFO, and produces statistical performance bounds as well. On the other hand, Bound III captures the instantaneous minimum server bandwidth consumption for the best bandwidth allocation at any given time, and thus provides tight lower bounds for the system along the time line. III. HEURISTIC ALGORITHMS To achieve the analytical bounds derived in the last section, we follow a practical approach to cache replacement and bandwidth allocation. These two strategies have to coordinate with each other seamlessly, as cache replacement also affects segment availability(i.e., the cached matrix C) and thus serves as a basis for bandwidth allocation. Moreover, they should be fast, effective, and distributed. In our system, HD movies are often partially stored in the local cache of some peers, so movie is not the suitable level for bandwidth allocation. An intuitive method is to migrate the water-leveling strategy from the movie level to the segment level for cache replacement [12], [13]. When removing a segment from the local cache of a peer, one can select the segment that is best globally provisioned, i.e., with the smallest global demand-to-supply ratio in terms of bandwidth. We refer to such strategy as best-globally-provisioned-first (BGPF), which is representative among a variety of least-recently-used and least-frequently-used strategies. For the corresponding bandwidth allocation, perfect-fair-sharing (PFS) is usually adopted by P2P systems due to its simplicity, where all the upload connections equally share the upload bandwidth of the peer [8], [17], [18]. At the segment level, we can let each segment in the local cache of a peer have an upload connection. As PFS-BGPF takes the global demand and supply into consideration, it should demonstrate the best performance. The drawbacks of PFS-BGPF are similar to our optimization solution. It is challenging to collect and calculate the demandto-supply ratio at the segment level in real time, as it can be highly dynamic. However, we still use it as the semipractical benchmark in our simulation. A different approach is to explore the temporal relationship of viewers in the same channel, which is referred to as stratification or chainbased approaches [15], [19] [21]. Each viewer only uploads to its closest followers in terms of the playback point within the channel, as to balance the upload workload of early and late viewers. Between different channels, usually following the Bandwidth Helping Principles, the peer bandwidth is allocated first to the channel they are currently watching [1], [13]. Help is offered to other channels only if the peers in the current channel are all satisfied, and they still have extra upload bandwidth. By applying such a temporal chain, it is demonstrated that peer upload bandwidth can be effectively utilized for a single movie [21], and multi-movie systems with homogeneous and moderate playback quality [1]. The principle of our strategy is simple. As derived in Bound II, the number of helpers is statistically in proportion to that of viewers for HD channels, so we do not explicitly balance 4

5 the demand and supply at the movie level. At the segment level, instead of using water-leveling approaches, we adopt a chain-based structure, and try to make the peer upload bandwidth as transferable as possible. For instance, as early viewers are always able to help late ones in the same channel, when allocating the bandwidth of helpers, we let them upload to the early HD viewers first. Later, the bandwidth of these early viewers can be allocated to following viewers, which transfers the bandwidth from the helpers to all the viewers. A. Peer Cache Management Considering that early HD viewers are requesting late segments, to meet the requests of such early HD viewers, it is desirable for HD helpers to store the last few segments rather than the beginning part of a movie. Therefore, at the segment level, a simple and natural FIFO replacement strategy is adopted, which pushes out early segments first. At the movie level, besides the simple FIFO cache replacement corresponding to Bound II, we can always let SD viewers keep the HD segments that have been watched before in order to provide sufficient HD segments in the system, which is referred to as passive caching. Recall that the peer cache can only store 1 HD movie or 2 SD movies at most, and the movie being watched must be stored in priority. As a result, each HD helper will always have the second-half segments of HD movies. If the helper starts to watch another HD movie, it will allocate its bandwidth within the HD channel first and thus may no longer serve as a helper. In this case, all the segments of the previous movies will be removed to make space for the new HD segments, where SD segments are still pushed out first. Note that such a peer cache management is easy to implement and requires no centralized coordination. In the case that a new HD movie is released in the system, its viewers will form a flash crowd, and the video content in the system is scarce at the beginning and the server has to provide a huge amount of bandwidth. Although the system can slowly converge to the steady state with passive caching, more active strategies can be adopted. For instance, the server can actively push the content of the new movie to potential helpers before it is released, i.e., active caching. Such a scenario has been studied through simulation [1], and we leave the modeling work for it as our future work. B. Peer Bandwidth Allocation Given the late HD segments cached by helpers, we need to find a way to allocate the bandwidth from helpers to viewers to transfer a portion of the available segments, and thus the upload bandwidth at the same time. Inappropriate allocation will result in nontransferable bandwidth. For instance, if the bandwidth of these helpers is allocated to late viewers in a channel, early viewers may suffer from insufficient supply, and the bandwidth of those late viewers will never be used by early viewers, as late viewers have no needed content. In this case, the content bottleneck occurs and the bandwidth is wasted. We propose an inter-chain algorithm to allocate the bandwidth of the helpers towards the viewers of an HD channel, such that the bandwidth wastage is reduced as much as possible. First, we find all the helpers that satisfy these conditions: 1) it is watching an SD movie and has extra upload bandwidth available; 2) it has cached the needed HD segments already. After that, these helpers are sorted in the ascending order based on the portion of HD segments they have. Helpers with a small portion of HD segments only have the last few segments, and thus can only support a small range of early viewers. To take this factor into account, such helpers will make decisions before others on selecting the HD viewers. The viewers are also sorted based on their arrival time in the channel chain, where early viewers will be served first until the bandwidth supply meets the streaming demand. The advantage is that the bandwidth allocated to early viewers can be transferred to following ones. The details are listed in Algorithm 1. Algorithm 1 Inter-chain bandwidth allocation 1: Assume there are m viewers as V = {v 1,v 2,...,v m } in an HD channel chain Ch, and set the current assigned streaming bandwidth d v i to for each viewer v i. 2: Find all helpers H = {h 1,h 2,...,h n } who have cached part of the HD movie already, and sort them in the ascending order based on the number of the cached HD video segments they have. Set the current available upload bandwidth u h i of all helpers to its available upload bandwidth after it has contributed to its own channel chain. 3: i 1 and j 1 4: while i n do 5: while j m do 6: if Helper h i has cached the segment that v j is watching and d v j < r H then 7: B needed r H d v j 8: if u h i B needed then 9: Assign all h i s upload bandwidth u h i to v j. 1: d v j dv j +uh i ; uh i ; 11: else 12: Assign part of h i s upload bandwidth to v j. 13: d j v r H ; u h i uh i B needed; j j +1 14: end if 15: end if 16: end while 17: i i+1 18: end while After the inter-chain allocation, the traditional inner-chain bandwidth allocation algorithm will be invoked. Early viewers will use the upload bandwidth to support late viewers, where the priority is still given to the viewers closer in their playback point. The server will compensate the bandwidth shortage, if no bandwidth or content is available from peers. For the details of this inner-chain algorithm, please refer to[1] and Lemma 3 therein. The inner-chain algorithm for SD channels is slightly different from that for HD chains. First, it will be invoked before SD viewers start to help HD channels. Moreover, an SD viewer may watch a movie already cached, such that there is no need to download again. We let these peers support the earliest viewers in that SD channel. The benefits are twofold: 5

6 SD Movie 2 ments SD Movie 1 ments HD Movie ments Inter-chain allocation: Early Inner-chain allocation: Early Helper 1 Helper 2 Helper 3 Helper 4 Helper n SD 2 S7 SD 2 S1 2 SD 1 S1 SD 1 S1 HD S2 HD S19 HD S18 Viewer1 2 Viewer1 SD 2 S3 SD 2 S2 SD 2 S1 SD 1 S1 SD 1 S1 HD S2 HD S SD 1 S1 SD 1 S1 HD S2 HD S11 11 SD 1 S1 SD 1 S1 HD S2 HD S SD 1 S2 SD 1 S1 HD S2 HD S19 HD S4 HD S3 1 Viewer 2 Viewer 3 Viewer 4 Viewer m Server Viewer 2 Viewer 3 Viewer Arrival Time t 1 4 Server Viewer m Arrival Time t Fig. 2: The inter and inner-chain bandwidth allocation 1) the server contribution for the earliest viewers in the original inner-chain allocation can be saved; 2) such bandwidth supporting the earliest viewers can be transferred to late viewers, who have a better chance of caching more HD segments. Through such an allocation strategy, the bandwidth of peers will eventually be transferred to where it is really needed, and thus the server intervention and bandwidth consumption is possibly minimized. Figure 2 illustrates an instance of the inter-chain and innerchain bandwidth allocation process. Assume the playback rates of the SD and HD movies are 5 Kbps and 1, Kbps, respectively, and the upload capacity of each peer varies from 4 Kbps to 8 Kbps. Helper 1 and 2 from channel SD 2 have cached several HD video segments, and are able to offer Kbps. Helper 3 and 4 from channel SD 1 have cached a half of the HD video segments, and each can provide 6 Kbps. Since Viewer 1 is watching ment 2 of the HD movie, all helpers can provide this segment. So Helper 1, 2 and 3 will assign all of their upload bandwidth to Viewer 1, and Helper 4 only needs to provide 2 Kbps to meet Viewer 1 s remaining bandwidth demand. As Helper 4 still has 4 Kbps extra bandwidth, it allocates all the remaining upload bandwidth to Viewer 2. After all the helpers have utilized their bandwidth, the earliest viewer (Viewer 1) locates the closest viewer that needs bandwidth (Viewer 3) and allocates all of its 6 Kbps. Following viewers will repeat the same process until they use up their bandwidth. C. Practical Issues If centralized, the time complexities of the inner and interchain allocation are O(n) and O(mn), respectively, where m is the number of helpers and n the viewers of a channel. For a more distributed implementation, the helpers and viewers Late Late TABLE II: The distribution of peer upload capacity Upload Capacity 8 Kbps 5 Kbps 4 Kbps Percentage 5% 3% 2% for a particular channel can be viewed as a small BitTorrentlike P2P swarm, where peers periodically exchange bitmap messages and maintain the overlay structure of the inter-chain system with the assistance of some functional tracker. The bandwidth allocation algorithm can be performed on a small number of such trackers selected from the peers in the channel, and these trackers will send messages to viewers including a list of the upstream candidates. If the intended upstream peer is currently busy serving other viewers, it can resort to the next available candidate on the peer list. The viewers and helpers can also maintain the overlay themselves through message exchange and make decisions locally based on the local knowledge of the inter-chain overlay in a fully distributed manner. In our heuristic algorithms, there is no need to collect or calculate the global demand-to-supply ratio for each segment. Only the bitmap of the segments of peers is exchanged as any typical P2P streaming systems. Therefore, we believe it will not introduce too much overhead to the system. A. System Setting IV. PERFORMANCE EVALUATION We developed a Java-based event-driven simulator to emulate a multi-channel PA-VoD system, which is extended from the widely-adopted BitTorrent simulator [22]. The playback rates of the SD and HD movies are 5 Kbps and 1, Kbps, respectively. The peer upload capacity follows the distribution listed in Table II, with an average of 63 Kbps. This setting is higher than the usual 53 Kbps [7], as the upload capacity of residential Internet accesses using DSL or Cable modem in North America nowadays is approaching 8 Kbps. There are 1 SD movies and 1 HD movies. Within each category, the popularity of the 1 movies follows a Zipf distribution with parameter 1, as such kind of distribution is widely observed in multi-channel online video systems [3], [23], [24]. For the stationary model, at the beginning of each simulation, we let peers (from N = 1, to,) join the system at the same time and never leave. To investigate how fast the server bandwidth consumption converges, we set the initial state of thesystemtobedifferentfromitssteadystate.eachpeerpicks a random segment of a random movie to watch, i.e., a uniform distribution among both movies and segments initially. All segments ahead of the picked segment are assumed to be stored in advance in a peer s local cache to its limit. We study three user viewing behaviors in the PA-VoD system. The transfer matrices P c between SD and HD categories are [.8.2;.8.2] for Case 1, [.9.1;.4.6] for Case 2, and [.5.5;.8.2] for Case 3. The channel popularity in the steady state of the three cases is illustrated in Fig. 3(a). Case 1 and Case 2 both imply the surplus mode, where the average peer upload capacity and streaming rate are 63 Kbps and 6 Kbps, respectively. Thus Bound I is calculated as zero. The two curves in the figure overlap with each other, 6

7 Case 1 Case 2 Case Case 1, Ana Case 1, Simu Case 2, Ana Case 2, Simu 1 3 Viewers, N=1, Helpers, N=1, Viewers, N=1, Helpers, N=1, Viewers, N=1, Helpers, N=1, Viewers, N=1, Helpers, N=1, Movie Popularity.15.1 Number of Helpers Number of Peers 1 2 Variation Coefficient Movie Index Movie Index Movie Index (a) Movie popularity in the steady state of the three cases (b) Number of helpers with two user viewing behaviors, FIFO (c) Distribution of HD viewers and helpers, Case 1, FIFO Fig. 3: Movie statistics and user behaviors (d) Variation coefficient of HD viewers and helpers, Case 1, FIFO which means the popularity of SD (channel 1 to 1) and HD (channel 11 to 2) channels in Case 1 and Case 2 are almost the same. However, different user behaviors are exhibited by these two cases. Compared with Case 2, peers in Case 1 are more active in transferring to a different category. Case 3 reflects the system in a deficit mode, i.e., not able to survive by the peer-contributed bandwidth even in the steady state, as a large portion of peers are watching HD movies. For each setting of these user behaviors, we evaluate a set of cache replacement and bandwidth allocation strategies, including our chain-based heuristics and PFS, with and without the corresponding passive cache replacement strategies, denoted by Chain-Passive, Chain-FIFO, PFS-BGPF, and PFS-FIFO, respectively. For small-scale system instances, we also use lp_solve for Java to obtain the optimal linear programming solution, which is corresponding to Bound III- FIFO or Bound III-Passive. B. Helper Peer Statistics In Case 1 (p c HS =.8), peers tend to transfer between HD and SD videos more frequently than Case 2 (p c HS =.4), and thus bring more helpers for HD channels, as demonstrated by the analytical and simulation results in Fig. 3(b). Here the cache replacement is a simple FIFO. We thus gain the insights that it is desirable to let peers transfer to SD channels immediately after they finish watching an HD movie. First, the overall bandwidth requirement will be reduced. Moreover, after watching an HD movie and transferring to an SD movie, the peer will have the HD content in its local cache, and thus is able to act as a helper to support HD viewers using its extra bandwidth. As it is shown that the popularity and the transfer probability of movies are controllable through a recommendation mechanism [23], [25], we can adopt a similar strategy to control p c HS. For example, the system can recommend related SD programs after a peer finishes watching an HD movie, or offer some form of rewards for transferring to SD movies or staying online. Fig. 3(b) also shows a slower ramp up process for Case 2, as peers in Case 2 are reluctant to transfer between categories. Fig. 3(c) plots the distribution of these helpers for N = 1, and N = 1, where we retrieve the statistics and calculate the mean values of HD channels in the steady state in Case 1. The simulation result shows that the number of helpers of an HD channel is always in proportion to the numbers of viewers, confirming the analytical results in Bound II. We refer to such phenomenon as the self-adaptivity of the system. Intuitively, if there are more viewers in an HD channel, after they finish the movie, many will transfer to SD channels with the cached HD content, and thus bring more helpers for the HD channel. The similar phenomenon is also observed in Fig. 3(b), where the number of HD helpers increases dramatically in the first four hours, as half of the peers are viewing HD movies at the beginning, and later become HD helpers. However, these channels demonstrate different levels of self-adaptivity, as shown by the coefficients of variation (the ratio of the standard deviation to the mean) in Fig. 3(d). Either a channel or the entire system with a smaller population suffers from a higher coefficient of variation, which indicates that the viewer and helper population is more unstable. We will detail its influence on the system performance in Section IV-D. C. System Performance in Stationary Scenarios The instantaneous server bandwidth consumption in the stationary scenarios is plotted in Fig. 4, with the peer population set to N = 1,, in order to avoid the long processing time of lp_solve. All of the strategies are assumed to be able to perform in real time in these scenarios. 1) Convergence Time: At the beginning of each simulation, HD viewers account for half of the overall peer population in the system due to the random pick of movies, which makes the system temporally staying in the deficit mode. After a short time (2 to 4 hours), the server bandwidth consumption decreases significantly. Recall that in Fig. 3(b), the number of helpers increases to a peak value in around 2 hours for Case 1, and 4 hours for Case 2, which is consistent to the convergence time here. Peers transfer more frequently in Case 1, and thus distribute more HD content faster. 2) Server Bandwidth Consumption: In Case 1 and Case 2, the peer-contributed bandwidth exceeds the total bandwidth demand, so Bound I reaches zero. However, Bound II is different for these two cases, and a more active transfer behavior between HD and SD channels (i.e., Case 1) leads to a lower Bound II. In Case 3, due to the large number of HD viewers, the system has bandwidth deficit even in the steady state, shown by the non-zero Bound I. Note that the chain-fifo approach is statistically bounded by Bound II, and Bound I and Bound II overlap with each other in all cases when passive caching is adopted, as it removes the 7

8 Case 1 Case 2 Case Chain FIFO Bound I Bound II Bound III FIFO Chain FIFO Bound I Bound II Bound III FIFO Chain FIFO Bound I Bound II Bound III FIFO Case 1 Case 2 Case Chain Passive Bound I, Bound II Bound III Passive Chain Passive Bound I, Bound II Bound III Passive Chain Passive Bound I, Bound II Bound III Passive Fig. 4: Server bandwidth consumption of the three cases in stationary scenarios content bottleneck. We find that the proposed chain-based heuristic algorithms perform generally well, and achieve lower server bandwidth consumption with passive caching as more helpers are present. Note that the total upload bandwidth of all peers is about 615 Mbps. The performance of the linear programming solution (Bound III) in these three cases demonstrates its optimality unsurprisingly, where the server bandwidth consumption can be even reduced to Bound I. The reasonisthatitattemptstofindthebestmatchbetweenhelpers and viewers, which does not necessarily follow the Bandwidth Helping Principles. Counter-intuitively, PFS-BGPF consumes much more server bandwidth than our chain-based heuristic algorithms in all cases. This is due to the small population of peers. Given N = 1, peers in the system, on average there willbe2hdviewers,andtheleastpopularhdchannelonly has a few viewers. The population of such channel is extremely unstable and it becomes even worse at the segment level, as each HD movie has 2 segments. Consider the case that peers havejustremovedthe1thsegmentofanhdmovieasnopeer is watching it. However, it is possible that those viewers are watching the 9th segment, and will request for the following one very soon. As the 1th segment is removed, there is no chance for it to return to the peers in a short time without active caching. Consequently, it becomes difficult for peers to catch up with the dramatic demand change at the segment level. We believe this is an important insight when designing bandwidth allocation algorithms for PA-VoD systems. D. System Scalability We also investigate the scalability of the system with the user behavior following Case 2. We vary the number of peers, and measure the bandwidth efficiency η in the steady state of each algorithm, which is visualized in Fig. 5(a). We find that such a system not only scales well, but also exhibits Bandwidth Efficiency (%) PFS FIFO Chain FIFO Chain Passive Number of Peers (a) Bandwidth efficiency under different peer population, Case 2 Percentage (%) Peer Population Chain FIFO Chain Passive Time Point (b) Peer population and bandwidth efficiency in diurnal arrival scenarios Fig. 5: User population dynamics a better performance under larger peer populations, which conforms to the smoothing effect of the large population in real systems [26]. Such a large population can better demonstrate the expected performance of each strategy, while in contrast a small population of peers examines the robustness of the algorithms against the peer churning between different channels and segments, as the system is more likely to deviate from its steady state. Once again our chain-based heuristic algorithms demonstrate the best performance, independent of the peer population, and passive caching helps further to reduce the server bandwidth consumption. The performance of PFS-BGPF is not comparable with our heuristic algorithms, and even worse than PFS-FIFO, in the small peer population cases. However, when the peer population increases, the system will become more stable, and PFS-BGPF will perform increasingly better. Given an sufficient number of peers in the system, PFS-BGPF will eventually demonstrate its capability of balancing the global demand and supply of each segment with the provision of global and local control information in real time, which is close to the performance of our heuristic algorithms, as illustrated when N = 1,. 8

9 E. Diurnal Arrival Scenarios Last but not the least, we evaluate the performance of the algorithms in a more dynamic scenario. Measurement studies have observed that VoD users usually follow the diurnal arrival pattern, with 12: PM to 2: PM and 7: PM to 11: PM as peak hours [1] [3], [24]. To emulate such phenomena, we generate N = 1, peers at the beginning of our simulation and set them as offline users. Then we randomly pick some of these offline users and let them join the system starting from 8: AM, following a non-homogeneous Poisson arrival process with time-dependent arrival rates. We carefully interpret the statistics from these measurement studies to set the arrival rate for each half an hour to reproduce a similar diurnal process, where the highest population of online users is reached at around 9: PM, and the second highest population at 2: PM, which is visualized as the percentage of online peers in Fig. 5(b). Once a peer finishes watching a movie, it will either leave the system with probability 5%, or stay online and pick another movie to watch. If the peer leaves the system, we assume it will keep the cached content and bring it back when returning to the system, which is a common practice in current PA-VoD systems. The transfer behavior of peers follows Case 1 in this section. 1) Prolonged Convergence Time: We first observe that the convergence time is prolonged to around 24 hours, which is due to the departure of helpers. However, such helping bandwidth is only temporarily lost as these helpers will return later with the previously-cached video content. After all peers have cached some HD video content, the system converges to its steady state. We thus suggest that encouraging peers to stay online as long as possible will accelerate such a process. 2) Effect of Online Population: PFS-BGPF clearly shows its vulnerability to peer churning, as its bandwidth efficiency varies significantly between valleys and peaks of the peer population. When there is a small population of online peers (i.e., the valleys), worse bandwidth efficiency is observed as the system is unstable and beyond the control of PFS-BGPF. This conforms to the insights we have from the stationary scenarios in Section IV-D. For the proposed algorithms, both Chain-Passive and Chain-FIFO strategies demonstrate a better robustness. In Case 1, peers are active enough to transfer between different movie categories, so there is little difference between the performance of Chain-Passive and Chain-FIFO. V. RELATED WORK The potential of utilizing peer-contributed resources in VoD systems has been studied by Huang et al. [7], with the conclusion that 95% of the server bandwidth consumption can be saved through a P2P solution. The fact also boosts a variety of practically deployed large-scale P2P VoD systems [2], [3], [27]. For a single-channel P2P VoD system, Parvez et al. [21] built models to compare different bandwidth allocation strategies and conjectured that a chain-based allocation is able to overcome the imbalance of bandwidth supply within a channel, and Yang et al. [28] proposed practical queuing techniques to overcome such imbalance. Ciullo et al. mathematically studied the model of chain-based allocation, under both stationary [15] and non-stationary scenarios [16]. The bandwidth allocation for BitTorrent-like systems has been studied by D Acuntoa et al. [14], where they characterized the trade-off between injecting new segments into the system and replicating existing ones under a flash-crowd scenario. For multi-channel live streaming systems, view-upload decoupling aims at allocating peer upload bandwidth across channels by decoupling the uploading content from the movie that a peer is watching [5], [6]. Linear programming models have also been built for the bandwidth allocation with several viewing behaviors [29]. Concerning multi-channel VoD systems, [8] [11] built different models to study the server bandwidth consumption with a limited cache size at each peer with homogeneous or heterogeneous peer upload capacity. However, these studies all assumed that channels are of homogeneous playback rates. Moreover, they focused on the movie-level analysis and did not study the case with HD movies that are partially cached. Working at the segment level, He et al. built linear programming models by assuming that helpers are given [13], and Wang et al. developed heuristic algorithms to locate them [12]. They both assumed that the global demand-to-supply information is available at the segment level. Our linear programming model differs from [13] as we do not specify helpers in advance but let the model locate the best candidates, and our heuristic algorithms are less dependent on the segment-level ratio than that in [12]. Instead, we make the bandwidth as transferable as possible among peers. VI. CONCLUSIONS AND FUTURE WORK In this paper, we studied the resource imbalance problem in PA-VoD systems with heterogeneous channel playback rates, where peers from SD channels help HD channels in terms of both upload bandwidth and cached content. Our model provided statistical performance bounds for the server bandwidth consumption with given viewing behaviors in the steady state, and instance bounds at any given time. Moreover, simple heuristic algorithms were proposed to efficiently allocate peer upload bandwidth within and across channels, by making it as transferable as possible. Simulation results verified that our heuristic algorithms reduced the server bandwidth consumption to the preferable theoretical lower bounds. Our ongoing and future work will consider the evolution of movie popularity, as measurement studies show that the long-term movie popularity is usually an exponentially decay function of the elapsed time [3], [24], [3], through a tracedriven simulation study. Moreover, in real systems the helper and viewer chains should be maintained in near-real time, or at least periodically. Therefore, we will examine the robustness of our algorithms in a more realistic environment on PlanetLab, where the real-time, fine-grained control information synchronization is largely absent from the system. Last but not least, as our work in this paper clearly indicates that transferring between SD and HD channels will help overcome the content bottleneck, a proper user incentive mechanism will be developed for PA-VoD systems. 9

10 ACKNOWLEDGEMENT The work is supported in part by NSERC of Canada, and Le Chang is also supported in part by a fellowship from China Scholarship Council. The authors would also like to thank the anonymous reviewers for their valuable comments. [29] M. Wang, L. Xu, and B. Ramamurthy. Linear programming models for multi-channel P2P streaming systems. IEEE INFOCOM, 21. [3] D. Niu, et al. Demand forecast and performance prediction in peerassisted on-demand streaming systems. IEEE INFOCOM, 211. REFERENCES [1] Y. Huang, T.Z.J. Fu, et al. Challenges, design and analysis of a largescale P2P-VoD system. In Proc ACM SIGCOMM, 28. [2] X. Hei, C. Liang, et al. A measurement study of a large-scale P2P IPTV system. IEEE Trans on Multimedia, 9(8): , 27. [3] Z. Liu, C. Wu, et al. UUSee: A large-scale operational on-demand streaming with random network coding. IEEE INFOCOM, 29. [4] G. Deng, T. Wei, et al. Measurement and modeling for QoS of VoD system. In Proc IEEE ICICIS, 211. [5] D. Wu, C. Liang, et al. View-upload decoupling: A redesign of multichannel p2p video systems. In Proc IEEE INFOCOM, 29. [6] D. Wu, Y. Liu, and K. Ross. Queuing network models for multi-channel P2P live streaming systems. In Proc IEEE INFOCOM, 29. [7] C. Huang, J. Li, and K.W. Ross. Can Internet video-on-demand be profitable? In Proc ACM SIGCOMM, pp , 27. [8] Y. Zhou, T.Z.J. Fu, et al. Statistical modeling and analysis of P2P replication to support VoD service. In Proc IEEE INFOCOM, 211. [9] Y. Zhou, T.Z.J. Fu, et al. A unifying model and analysis of P2P VoD replication and scheduling. In Proc IEEE INFOCOM, 212. [1] W. Wu and J. Lui. Exploring the optimal replication strategy in P2P- VoD systems: characterization and evaluation. In Proc 3th IEEE International Conference on Computer Communications (INFOCOM 11), pp , 211. [11] B. Tan and L. Massoulié. Optimal content placement for peer-to-peer video-on-demand systems. In Proc IEEE INFOCOM, 211. [12] Z. Wang, C. Wu, L. Sun, and S. Yang. Strategies of collaboration in multi-channel P2P VoD streaming. IEEE GLOBECOM, 21. [13] Y. He and L. Guan. Solving streaming capacity problems in P2P VoD systems. IEEE Transactions on Circuits and Systems for Video Technology, 2(11): , 211. [14] L. D Acunto, T. Vinkó, and H. Sips. Bandwidth allocation in BitTorrentlike VoD systems under flashcrowds. IEEE P2P, 211. [15] D. Ciullo, et al. Stochastic analysis of self-sustainability in peer-assisted VoD systems. In Proc IEEE INFOCOM, 212. [16] D. Ciullo, et al. Performance analysis of non-stationary peer-assisted VoD systems. In Proc IEEE INFOCOM mini-conference, 212. [17] W.-C. Liao, F. Papadopoulos, and K. Psounis, Performance analysis of BitTorrent-like systems with heterogeneous users. Performance Evaluation, 64(9 12): , 27. [18] A. Chow, L. Golubchik, and V. Misra, BitTorrent: an extensible heterogeneous model. In Proc IEEE INFOCOM, pp , 29. [19] T. Do, et al. P2VoD: providing fault tolerant video-on-demand streaming in peer-to-peer environment. In Proc IEEE ICC, 24. [2] A. Gai, F. Mathieu, et al. Stratification in P2P networks application to BitTorrent. ArXiV CS/61213, 26. [21] N. Parvez, C. Williamson, A. Mahanti, and N. Carlsson. Analysis of BitTorrent-like protocols for on-demand stored media streaming. In Proc ACM International Conference on Measurement and Modeling of Computer Systems (SIGMETRICS 8), pp , 28. [22] A. Bharambe, C. Herley, and V. Padmanabhan. Analyzing and improving BitTorrent performance. In Proc IEEE INFOCOM, 26. [23] H. Yu, D. Zheng, B.Y. Zhao, and W. Zheng. Understanding user behavior in large-scale video-on-demand systems. EuroSys, 26. [24] M. Allen, B. Zhao, and R. Wolski. Deploying video-on-demand services on cable networks. In Proc IEEE ICDCS, pp , 27. [25] X. Cheng and J. Liu. Exploring interest correlation for peer-topeer socialized video sharing. In ACM Transactions on Multimedia Computing, Communications, and Applications, vol. 8, no. 1, article 5, 212. [26] C. Griwodz, M. Bär, and L. Wolf. Long-term movie popularity models in video-on-demand systems: or the life of an on-demand movie. In Proc 5th ACM International Conference on Multimedia(Multimedia 97), pp , [27] X. Hei, Y. Liu, and K.W. Ross. Inferring network-wide quality in P2P live streaming systems. IEEE Journal on Selected Areas in Communications, 25(9): , 27. [28] Y. Yang, A. Chow, L. Golubchik, and D. Bragg. Improving QoS in BitTorrent-like VoD systems. In Proc IEEE INFOCOM, 21. Le Chang is currently a PhD candidate in the Department of Computer Science at the University of Victoria, British Columbia, Canada. He received his Bachelors and Masters degrees in computer science from Central South University, Changsha, China. His current research interests include the modeling, design, measurement and implementation of P2P VoD systems. Jianping Pan is currently an associate professor of computer science at the University of Victoria, Victoria, British Columbia, Canada. He received his Bachelor s and PhD degrees in computer science from Southeast University, Nanjing, Jiangsu, China, and he did his postdoctoral research at the University of Waterloo, Waterloo, Ontario, Canada. He also worked at Fujitsu Labs and NTT Labs. His area of specialization is computer networks and distributed systems, and his current research interests include protocols for advanced networking, performance analysis of networked systems, and applied network security. He received the IEICE Best Paper Award in 29, the Telecommunications Advancement Foundation s Telesys Award in 21, the WCSP 211 Best Paper Award and the IEEE Globecom 211 Best Paper Award, and has been serving on the technical program committees of major computer communications and networking conferences including IEEE INFOCOM, ICC, Globecom, WCNC and CCNC. He is a senior member of the ACM and a senior member of the IEEE. Min Xing is currently a Ph.D student in the Department of Electrical and Computer Engineering, University of Victoria, British Columbia, Canada. He received B.S. degree in Computer Science from Soochow University, Suzhou, Jiangsu in 27, and M.S. degree in Software Engineering from Tongji University, Shanghai, China in 21. His current research interests include multimedia over networks and TCP incast collapse problems in cloud computing and datacenters. 1