The production of peer-to-peer video-streaming networks

Transcription

1 The production of peer-to-peer video-streaming networks Dafu Lou Yongyi Mao Tet H. Yeap SITE, University of Ottawa, Canada SIGCOMM 07 P2P-TV, August 31, 2007, Kyoto, Japan.

2 Outline Problem 1 Problem Dynamics of user for P2P Video Streaming Networks 2 System Model Definitions 3 A Lower Bound of Production Proof:Protocol A 4 Protocol A Protocol B

3 P2P Video Streaming Networks Dynamics of user for P2P Video Streaming Networks

4 P2P Video Streaming Networks Dynamics of user for P2P Video Streaming Networks

5 P2P Video Streaming Networks Dynamics of user for P2P Video Streaming Networks

6 P2P Video Streaming Networks Dynamics of user for P2P Video Streaming Networks

7 P2P Video Streaming Networks Dynamics of user for P2P Video Streaming Networks

8 P2P Video Streaming Networks Dynamics of user for P2P Video Streaming Networks

9 P2P Video Streaming Networks Dynamics of user for P2P Video Streaming Networks

10 Dynamics of user for P2P Video Streaming Networks Dynamics of users for P2P video streaming networks It is an exponential function.

11 Dynamics of user for P2P Video Streaming Networks Dynamics of users for P2P video streaming networks It is an exponential function. What is the mathematical formula? No answer yet. Related to protocols. non-linear.

12 Dynamics of user for P2P Video Streaming Networks Dynamics of users for P2P video streaming networks It is an exponential function. What is the mathematical formula? No answer yet. Related to protocols. non-linear. The problem becomes linear for using Fountain Codes rateless coding.

13 Fountain Codes for Video Streaming Dynamics of user for P2P Video Streaming Networks Video stream encoded using Fountain Codes

14 Fountain Codes for Video Streaming Dynamics of user for P2P Video Streaming Networks Video stream encoded using Fountain Codes Generate an infinite sequence of encoded packets for each video block.

15 Fountain Codes for Video Streaming Dynamics of user for P2P Video Streaming Networks Video stream encoded using Fountain Codes Generate an infinite sequence of encoded packets for each video block. Decode the video block from any received approximately the same number of the bits as the video block.

16 Fountain Codes for Video Streaming Dynamics of user for P2P Video Streaming Networks Video stream encoded using Fountain Codes Generate an infinite sequence of encoded packets for each video block. Decode the video block from any received approximately the same number of the bits as the video block. Do not need to know the statistics of packet loss.

17 Fountain Codes for Video Streaming Dynamics of user for P2P Video Streaming Networks Video stream encoded using Fountain Codes Generate an infinite sequence of encoded packets for each video block. Decode the video block from any received approximately the same number of the bits as the video block. Do not need to know the statistics of packet loss. The sum of the link capacities along all links can be achieved.

18 System Model Problem System Model Definitions Video server: M video blocks. Arrived users: N(t). User uploading bandwidth: b bits/second. Server uploading bandwidth: s bits/second.

19 Definition Production System Model Definitions Definition (Production) For any given network and under any given video-streaming protocol, the production N m (t) of block m at time t is defined as the number of users that have obtained block m by time t.

20 System Model Definitions Definition Production Potential Definition (Production Potential) Under any given video-streaming protocol, the production potential S m (t) of block m at time t is defined by S m (t) := 1 γ A t 0 (s m (τ) + b m (τ)n m (τ)) dτ, where s m (t) and b m (t), depending on the protocol, are respectively the server s output bandwidth allocated to transmitting block m at time t and the average user output bandwidth allocated to transmitting block m at time t, where the average is the overall users having obtained block m.

21 Definition Saturation System Model Definitions Definition (m-unsat and Saturation Time) At any time T, the system is said to be block-m-unsaturating, or m-unsat, if for any t [0, T ], N m 1 (t) > S m (t), or N m 1 (t) = S m (t) = 0. where N 0 (t) := N(t). The saturation time T m of block m is defined as T m := sup{t : the system is m UNSAT at T }.

22 Saturation Time Problem System Model Definitions For a practical P2P protocol, the saturation time has the following properties: T m is finite for every m and as small as possible.

23 Saturation Time Problem System Model Definitions For a practical P2P protocol, the saturation time has the following properties: T m is finite for every m and as small as possible. At time t > T m, N m (t) is close to N(t).

24 A Lower Bound of Production A Lower Bound of Production Proof:Protocol A Assumption: λ T 1 > e. (1)

25 A Lower Bound of Production A Lower Bound of Production Proof:Protocol A Assumption: λ T 1 > e. (1) Theorem Under above assumption, there exists a transport protocol such that ) 1 N m (t) min (λt, e b(1 γ) AM (t Tm) u(t T m ) for all m {1, 2,... M}, where and 2 Tm is finite for every m. T m = ma/(1 γ)s + 1/λ;

26 Proof of Theroem: Protocol A A Lower Bound of Production Proof:Protocol A We prove Theorem 1 by constructing a protocol(protocol A) to induce a linear-system dynamics. Protocol A. Server only provides video blocks to the first arrived user. Every user requests video blocks in sequence. Every user allocates the same fraction of its output bandwidth for distributing each block.

27 Proof of Theroem: Protocol A A Lower Bound of Production Proof:Protocol A We prove Theorem 1 by constructing a protocol(protocol A) to induce a linear-system dynamics. Protocol A. Server only provides video blocks to the first arrived user. Every user requests video blocks in sequence. Every user allocates the same fraction of its output bandwidth for distributing each block. Prove the result by induction.

28 A Lower Bound of Production A Lower Bound of Production Proof:Protocol A Corollary There exists a fountain-coded transport protocol such that T m T A m, for all m {1, 2,... M}.

29 Protocol A Protocol B Simulated production achieved by Protocol A and Theoretical results of Theorem 1 Production N m (t) λ =1/4, γ =2%, M=3, s=5mbps, b=5mbps, A= 14M bytes, protocol A Block 1(Simulated) Block 2 (Simulated) Block 3 (Simulated) Block 1 (Theoretical) Block 2 (Theoretical) Block 3 (Theoretical) 50 Block 1 Block 2 Block Time (s)

30 Protocol A Protocol B Simulated production achieved by Protocol A and Theoretical results of Theorem 1 Derivative of production (t) N m λ =1/4, γ =2%, M=3, s=5mbps, b=5mbps, A= 14M bytes, protocol A Block 1 Block 2 Block 3 Block 1 (Simulated) Block 2 (Simulated) Block 3 (Simulated) Block 1 (Theoretical) Block 2 (Theoretical) Block 3 (Theoretical) Time (s)

31 Protocol B extend for more practical settings Protocol A Protocol B Server keeps supplying video blocks to users. Every user allocates the output bandwidth for each block dynamically.

32 Protocol A Protocol B Simulated production achieved by Protocol B and the lower bounds of Theorem 1 Production N m (t) λ =1/4, γ =2%, M=10, s=20mbps,b=1mbps, A=14M bytes, β=3.75mbps, protocol B Block 1 (Simulated) Block 5 (Simulated) Block 10 (Simulated) Block 1 (Theoretical) Block 5 (Theoretical) Block 10 (Theoretical) Block 5 Block Time (s) Block 1 Block 1 Block 5 Block 10

33 Protocol A Protocol B Simulated production achieved by Protocol B and the lower bounds of Theorem 1 Derivative of production N m (t) Block 1 Block 5 λ =1/4, γ =2%, M=10, s=20mbps,b=1mbps, A=14M bytes, β=3.75mbps, protocol B Block 10 Block 1 (Simulated) Block 5 (Simulated) Block 10 (Simulated) Block 1 (Theoretical) Block 5 (Theoretical) Block 10 (Theoretical) Block 10 Block 5 Block Time (s)

34 Problem Study the dynamics of P2P video streaming networks based on fountain codes. Introduce production to characterize the system dynamics. Theroetical results have been presented based on the production. Simulation results have also been compared finnally.