A new caching policy for cloud assisted Peer-to-Peer video on-demand services

Transcription

1 A new caching policy for cloud assisted Peer-to-Peer video on-demand services Franco Robledo, Pablo Rodríguez-Bocca, Pablo Romero and Claudia Rostagnol Facultad de Ingeniería, Universidad de la República. Montevideo, Uruguay. IEEE International Conference on Peer-to-Peer Computing September 03-05, Tarragona, Spain

2 Outline 1 Introduction and Problem 2 Proposed Solution 3 Problem Optimization 4 Experimental Evaluation 5 Conclusions

3 Outline 1 Introduction and Problem 2 Proposed Solution 3 Problem Optimization 4 Experimental Evaluation 5 Conclusions

4 Problem Problem - first definition Problem We have a set of videos that we want to distribute on-demand, using GoalBit P2P protocol ( optimizing resources and download time. In order to better understand the problem we have to define the following concepts: GoalBit platform, protocol and components. Peers behavior. Previous work. Assumptions.

5 Definitions What is GoalBit? GoalBit is a set of products and protocols: GoalBit Protocol (GBTP) based on BitTorrent protocol, but designed for live streaming. GoalBit Media Player (GMP) player to watch live and on-demand GoalBit contents. GoalBit Media Server (GMS) which can: play a GoalBit streaming, distribute a GoalBit streaming, generate a GoalBit streaming (broadcast), and transcode a GoalBit streaming. GoalBit Suite (GS) that is a web system to administrate and control a GoalBit Platform.

6 Definitions GoalBit VoD components These are the GoalBit components related with P2P Protocol and on-demand distribution: Content: video to be distributed on demand. Peer: end-user that want to watch a video (downloader or seeder) Super-Peer: special peer with better bandwidth and more stable. They are managed by the platform s operator and only executed in the cloud servers.

7 Definitions GoalBit VoD components Tracker: server entity that knows all Peers and Super- Peers that are sharing a content (seeding or downloading). Repository: storage space where to save VoD contents (inside the GoalBit platform) to be distributed by Super- Peers.

8 Definitions Peers behavior About peers behavior in a BitTorrent-like system: Peers can enter and leave the network when they want. A peer can be in one of the following states: connecting, downloading, seeding or disconnected. We can estimate the probabilities of changing from one state to other. It was previously shown 1 that the BitTorrent peers behavior can be modeled as a Markov chain. 1 Y. Tian, D. Wu, and K. W. Ng, Analyzing multiple file downloading in bittorrent in Proceedings of ICPP 06 - IEEE, August 2006, pp

9 Our goal Problem - formal definition Now we can present our problem in a more detailed way: Problem We have a set of videos, a set of repositories and super-peers (servers) and a set of peers requesting to watch these videos on demand. We want to find the best video distribution into the repositories to offer a minimal download time to peers (which could imply to add more replicas for more popular/required videos and less replicas for less popular videos).

10 Outline 1 Introduction and Problem 2 Proposed Solution 3 Problem Optimization 4 Experimental Evaluation 5 Conclusions

11 Some details Details As proposed in previous work, we model the system as a Markov chain with following details: Each peer can download multiple streams at time t. Peers are grouped into classes: {C 1, C 2,..., C K } (peers in class C i are downloading i videos simultaneously). Peers at class C i allocate the i-th part of its peer s bandwidth for each concurrent download. Video popularity is defined by the number of peers requesting the same video in a period of time.

12 Problem data Problem data K available videos s j size (in kbits) of video j xj i(t) downloaders in class Ci downloading video j at time t yj i(t) seeders in class Ci seeding video j at time t spj i(t) super-peers in class Ci seeding video j at time t λ i j arrival rate for peers in class C i requesting video j γ departure rate of seeders θj i departure rate of downloaders in class C i downloading video c total download bandwidth for each peer (in kbps) µ total upload bandwidth for each peer (in kbps) ρ total upload bandwidth for each super-peer (in kbps) η video sharing effectiveness between peers (η [0, 1]) S p storage capacity of super-peer p (in kbits) E p j indicates if the super-peer p has a copy of video j (E p j 0, 1)

13 Problem model Problem model (P2P) Modeling the peers behavior as a simple fluid model we get the following differential equations (peers evolution: xj i (t) and y i j (t)): P2P Fluid model dx i j dt dy i j dt = λ i j θ i x i j min = min { { c is j x i j, η µ is j x i j + α i j c is j x i j, η µ is j x i j + α i j k ( µ yj k s j k k + ρ spj k s j k ( µ yj k s j k + ρ spj k s j k )} γ i j y i j )} i, j {1... K }:

14 Problem model Problem model (P2P) Assuming that the system will reach its steady state, where the number of peers is stable ( dx j i dt = dy j i dt can calculate the steady state value for x i j = 0 i, j {1... K }), we (t) and y i j (t): P2P Steady state x i j = max{ λi j is j P2P c y i j P2P = λi j γ, iλi j γµη λ k j k k λk j γs j k λk j µ k γρ k z k j k }

15 Problem model Problem model (CDN) A traditional Content Delivery Network (CDN) 2 can be viewed as a particular case of this analytical approach (where η = 0, µ = 0, yj i (t) = 0 and the previously named super-peers are now static servers). CDN Fluid model dx i j dt = λ i j θj i x j i min{ c xj i is, ρ sp +αi j k j j s j k } k i, j {1... K } 2 CDN is a large distributed system of servers deployed in multiple data centers over Internet. Its goal is to serve content to end-users with high availability and high performance.

16 Problem model Problem model (CDN) To get the expressions for the steady state in the CDN system we take µ = 0 and η = 0: Steady state { λ i xj i j is j = max CDN c, iλi j (λ } j ρ j ) θλ j

17 Problem model Average download time The average download time for any downloader at steady state can be computed applying Little s law: T i j = x j i λ i j We denote T P2P and T CDN the expected download times under steady state for peers in a P2P network and users in the CDN system, respectively. Average download time. T P2P = x i j P2P λ i j T CDN = x i j CDN λ i j

18 Problem model Average download time So, to compare average download times we can compare the number of downloaders in steady state for each system. We demonstrate that the following chain of inequalities holds: j = iλi j (λ j ρ j ) iλ i j φ j ( ) iλi j (λ j ρ j ) P2P λ j θ + µ s j (η θ γ ) θλ j x i = x i j CDN So we can conclude a very important result: P2P vs. CDN T P2P T CDN

19 Outline 1 Introduction and Problem 2 Proposed Solution 3 Problem Optimization 4 Experimental Evaluation 5 Conclusions

20 Optimization Combinatorial Optimization Problem Our problem can now be written as a Combinatorial Optimization Problem (COP): Combinatorial Optimization Problem min E p j K max j=1 s.t. λ j s j c (1) j, λ j ρ j φ j θ + ηµ µθ s j γs j E p j s j S p p (2) p E p j 2 j (3)sp j = p E p j j (4)E p j {0, 1} j, p

21 Optimization Multi-Knapsack Problem The COP we address here is similar to the Multi-Knapsack Problem (MKP), where each super-peer holds a knapsack (super-peers storage) with limited capacity and items (videos) must be placed inside the knapsacks. Since MKP is known to be Strongly NP-Hard (it reduces to the Bin Packing Problem 3 ) we designed a Greedy Randomized Adaptive Search Procedure (GRASP). 3 M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. New York, NY, USA: W. H. Freeman & Co., 1979.

22 Optimization Greedy Randomized Adaptive Search Procedure GRASP is an iterative process which operates in two phases: 1 Construction Phase: an initial feasible solution is built, 2 Local Search Phase: solution s neighborhood is explored to find better solutions. As a result we will get a possible distribution of videos in the available super-peers, which gives the best (minimum) download time of all tested solutions.

23 Implementation GRASP - Construction Phase E = RandomGreedy(λ, θ, γ.η, s, S, µ, c, ρ) 1: V = SortVideos(s) 2: for j = 1 TO K do 3: (p 1, p 2, p 3 ) FeasibleSelect(S 1,..., S P ) 4: E(p 1, V (j)) 1 5: E(p 2, V (j)) 1 6: if p 3 > 0 then 7: E(p 3, V (j)) 1 8: end if 9: Update(S 1,..., S P ) 10: end for 11: return E

24 Implementation GRASP - Local Search Phase E out = LocalSearch(E) 1: (E, improve) Add(Rand(SP, Video)) 2: IF improve GO TO Line 1 3: (E, improve) Delete(Rand(SP, Video)) 4: IF improve GO TO Line 1 5: (E, improve) Swap(Rand(SP1, V 1), Rand(SP2, V 2)) 6: IF improve GO TO Line 1 7: return E out = E

25 Outline 1 Introduction and Problem 2 Proposed Solution 3 Problem Optimization 4 Experimental Evaluation 5 Conclusions

26 Tests GRASP - Evaluation Real information from a local Internet Video on-demand Service Provider (AdinetTV videos (K ), videos average size is 23 MB (s), 4 super-peers (P), super-peers storage capacity is 1500 GB (S), super-peers upload rate is 10 Mbps.(ρ), peers download rate is 1 Mbps (c), peers upload rate is 0.25 Mbps (µ), P2P effectiveness of 50% (η = 0.5), seeders departure with rate 100 (γ = 100) and peers departure with rate 0.1 (θ = 0.1).

27 Tests GRASP - Implementation We implemented the COP in Matlab, and we calibrate the GRASP algorithm with generated instances. We contrast the performance of both CDN and P2P system in two aspects: scalability: we stress the system keeping the popularity proportional with the real data (i.e. multiplying the real λ by an increasing factor). economical savings: we chose a fixed value for the system popularity and then changed the number of super-peers/servers (increasing the available resources at the platform side).

28 Results GRASP - Scalability result Estimated download time (CDN) T_P2P T_CDN Popularity factor (10^i) Estimated download time (P2P) Figure: Performance of CDN and P2P systems versus popularity.

29 Results GRASP - Savings result Estimated download time (CDN) T_P2P T_CDN Number of super-peers Estimated download time (P2P) Figure: P2P performance versus number of super-peers.

30 Outline 1 Introduction and Problem 2 Proposed Solution 3 Problem Optimization 4 Experimental Evaluation 5 Conclusions

31 Results theory: We theoretically shown that, under same conditions, the average download time of the P2P system is equal or better than the average download time of CDN system. scalability: We confirmed the theory in the practice - In order to reach the same level of service (the same average download time) in a client-server system we should increase the number of servers (or super-peers) proportionally with the end-user requests; while in the P2P system we have a natural scalability with the growing resources offered by users (downloaders and seeders). savings: Results showed that CDN system is much more sensible to the changes in the available resources (super-peers/servers).

32 Future work Current and future goals: Compare our GRASP results with other metaheuristics in order to find a good approximation of the optimal solution. Include the optimization algorithm into GoalBit Platform in order to know the algorithm performance and adaptation to the real world. Gather data from popular commercial services to further validate our model.

33 Thanks! UdelaR: GoalBit: AdinetTV: