Mathematical Analysis of Scheduling Policies in Peer-to-Peer Video - PowerPoint PPT Presentation

Motivation Contributions Video on-demand Live Streaming Conclusions Mathematical Analysis of Scheduling Policies in Peer-to-Peer Video Streaming Networks Pablo Romero Facultad de Ingeniería, Universidad de la República. PEDECIBA Informática, Montevideo, Uruguay. Advisors: Dr. Ing. Franco Robledo (Universidad de la República) Dr. Ing. Pablo Rodríguez-Bocca (Universidad de la República) Ph.D. Thesis Defense, November 19 th , 2012 1 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Outline Motivation 1 Contributions 2 Video on-demand 3 Live Streaming 4 5 Conclusions 2 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Outline Motivation 1 Contributions 2 Video on-demand 3 Live Streaming 4 5 Conclusions 3 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Services Video Distribution in Internet Video streaming modes File sharing: full download is mandatory before playback. Video on-demand: progressive and asymmetric playback. Live Streaming: simultaneous generation, distribution and synchronized playback. Hint In this thesis we focus on the most challenging streaming modes: Video on-demand (VoD) and Live streaming (Live). 4 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Services Video Distribution in Internet Video streaming modes File sharing: full download is mandatory before playback. Video on-demand: progressive and asymmetric playback. Live Streaming: simultaneous generation, distribution and synchronized playback. Hint In this thesis we focus on the most challenging streaming modes: Video on-demand (VoD) and Live streaming (Live). 4 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Video On-Demand Video on-demand Context A 10% of Internet Traffic is due to YouTube videos. Google pays more than 1 million dollars per day for bandwidth access. YouTube still does not exploit idle resources from end-users. Hint A mathematical analysis of user-assistance in VoD services is attractive. 5 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Video On-Demand Video on-demand Context A 10% of Internet Traffic is due to YouTube videos. Google pays more than 1 million dollars per day for bandwidth access. YouTube still does not exploit idle resources from end-users. Hint A mathematical analysis of user-assistance in VoD services is attractive. 5 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Live Streaming Live Streaming Context BitTorrent is suitable for offline, but live services... The most successful P2P systems are BitTorrent-based. Pull-mesh systems represent the most promising distribution engine. Hint A mathematical analysis of pull-mesh cooperative services is attractive. 6 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Live Streaming Live Streaming Context BitTorrent is suitable for offline, but live services... The most successful P2P systems are BitTorrent-based. Pull-mesh systems represent the most promising distribution engine. Hint A mathematical analysis of pull-mesh cooperative services is attractive. 6 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Outline Motivation 1 Contributions 2 Video on-demand 3 Live Streaming 4 5 Conclusions 7 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Main Contributions Video On-Demand Video On-Demand Mathematical modeling of user-assisted VoD systems. 1 Analysis of expected evolution. 2 Analysis of global stability (sequential VoD systems). 3 Cooperative systems always outperform raw CDN 4 technology. Combinatorial specification of a Caching Problem. 5 Resolution and application in YouTube 6 (real-world simulation). 8 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Main Contributions Live Streaming Live Streaming Mathematical analysis of chunk scheduling policies 1 (pull-mesh cooperative model). Design of the best policies so far. 2 Introduction of feasible policies in GoalBit. 3 Design of a Multi-Class model, regarding free-riding and 4 heterogeneity. 9 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Outline Motivation 1 Contributions 2 Video on-demand 3 Live Streaming 4 5 Conclusions 10 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Model Objective The Goal Consider a set of video items, super-peers (resourceful stable peers) with repositories and joining users requesting videos on demand. We want to find the best video assignment into the repositories, in order to offer a minimal download time to end-users. Note A special treatment to popular videos and large files is required. 11 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Model VoD components (1/2) Content : video to be distributed on demand. Peer : end-user that wants to watch one or several video items ( downloader or seeder ) Super-peers : resourceful stable peers managed by the op- erator Repository : limited storage space where to save VoD con- tents to be distributed by Super-Peers . Tracker : server entity that knows all Peers and Super- Peers that are sharing a content (seeding or downloading). 12 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Model VoD components (2/2) 13 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Model Definitions As proposed in related literature, we model the system as a Markov chain with following details: K video items with sizes s 1 , ..., s K (measured in Kbits). 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 set’s cardinalities: j ( t ) : downloaders in class C i downloading video j at time t x i j ( t ) : seeders in class C i seeding video j at time t y i j ( t ) : super-peers in class C i seeding video j at time t z i Markov chain hypothesis: Peers join the network following a poissonian process, and abort the system with an exponential law. Seeders depart the system exponentially. 14 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Model Other model parameters arrival rate for downloaders in class C i requesting video j λ i j departure rate of downloaders in class C i downloading video j θ i j departure rate of seeders in class C i requesting video j γ i j c i download bandwidth for each peer in the class C i j requesting video j (in kbps ) µ i upload bandwidth for each peer in the class C i j seeding video j (in kbps ) ρ i upload bandwidth for each super-peers in the class C i j seeding video j (in kbps ) η video sharing effectiveness between peers ( η ∈ [ 0 , 1 ] ) 15 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Model General Fluid Model (GFM) Modeling the expected peers’ behavior as a deterministic fluid model, we get the General Fluid Model (peers evolution: x i j ( t ) and y i j ( t ) ): GFM ˙ j = λ i j − θ i j x i j − min { c i j x i j , ηµ i j x i � ( µ k j y k j + ρ k j z k  x i j + j ) } ,    k ˙ � j = min { c i j x i j , ηµ i j x i ( µ k j y k j + ρ k j z k j ) } − γ i j y i y i j + j .    k where i , j ∈ { 1 , . . . , K } . The complexity and number of variables involved makes the GFM hard to treat analytically. 16 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Model Concurrent Fluid Model (P2P-CFM) BitTorrent-based Assumptions “Fair transmission”: the resources are equally distributed in 1 the different concurrent videos: “Tit-for-tat”: proportional downloading according to the 2 level of altruism. “Fair Seeders”: seeders send a rate proportional to 3 download bandwidth and population. “Fair Super-peers”: super-peers send a rate proportional to 4 download bandwidth and population. “Peers Departures”: peers and seeders depart following 5 the Zipf law . 17 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Model Video on-demand Sub-Models and Relations GFM Fairness P2P-CFM Single item No Cooperation P2P-SFM CDN-CFM No Cooperation Single item CDN-SFM 18 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Sequential fluid model P2P-SFM - Rest Point dx i dy i j j We find the only rest point solving the system dt = dt = 0: Rest Point for the P2P-SFM � θ s j + c , λ j ( γ s j − µ ) − γρ z j λ j s j � P 2 P x j SFM = max θ ( γ s j − µ ) + ηγµ P 2 P SFM = λ j − θ x j P 2 P SFM y j . γ j CDN P 2 P The rest point for the CDN-SFM is just x j SFM = x j SFM | µ = 0 . Global Stability Theorem The P2P-SFM is Globally Stable (whenever γ > 0). 19 / 47

Motivation Contributions Video on-demand Live Streaming Conclusions Sequential fluid model Expected waiting time The expected waiting time for any downloader under regime can be computed applying Little’s law: E { T j } = x j λ j . Then, the expected waiting time of a user T SFM P 2 P and T SFM CDN are: Expected waiting time SFM = 1 SFM = 1 � P 2 P � CDN � T P 2 P T CDN x j SFM , x j SFM , where λ = λ j . λ λ j j j Domination Theorem T P 2 P SFM ≤ T CDN SFM . 20 / 47