Playback delay in p2p streaming s ystems with random packet forwarding

1. Playback delay in p2p streaming systems with random packet forwarding Viktoria Fodor and Ilias Chatzidrossos Laboratory for Communication Networks School of Electrical Engineering KTH, Royal Institute of Technology

2. P2P Multimedia Streaming • Peer-to-peer system • peers contribute with transmission bandwidth and processing power • system transmission capacity scales as the number of peers increases • Peer-to-peer live streaming • newly generated content has to be propagated to all peers with low delay • Different from offline content distribution • strict delay requirements FMN 2008

3. Context of this work • We propose streaming algorithms for mesh based streaming systems • Build an analytic framework for performance evaluation • Verify the validity of our model • Derive playback delay – playout continuity charactersitics FMN 2008

4. Mesh based overlays (I) • Peers are organized in a mesh (grid) • There is minimal overhead in maintaining the overlay • Each peer has a set of neighboring peers that it communicates and exchanges data with • Each data chunk in a mesh overlay goes down a spanning tree to reach all peers. That tree is different for every packet FMN 2008

5. Mesh based overlays (II) • Different forwarding schemes • Push: a peer decides which data to send to which neighbor • Pull: a peer explicitly asks for specific data from a neighbor • Hybrid: mixture of the above schemes How do peers know whether some of their neighbors have a specific packet or not? FMN 2008

6. Buffer contents and buffer maps • All peers have a buffer to absorb variations in packet delivery times • Any of the packets that a peer has in its buffer could be potentially sent to some of its neighbors • Data exchange between neighbors is based on information that they have on each others buffer contents • A buffer map is a compact representation of a peer’s buffer, suitable for sending to other peers FMN 2008

7. Push scheduling algorithms • Random scheduling: • Peer constructs the list of neighbors that are missing at least one packet that itself has • Chooses randomly one of them to forward to. • Chooses randomly one missing packet to send • Priority Scheduling: • Peer selection same as in the previous case. • Once the neighbor is chosen, the ”oldest” missing packet is sent FMN 2008

8. System description • No playback lag among peers • At any point in time peers have the same limits for their buffers • Time is slotted • Length of a time-slot equal to a packet duration time • All transmissions occur within a time-slot • Synchronous and Asynchronous schemes • Static Overlay • Streaming server • Upload capacity = m * streaming rate • N peers • Upload capacity = streaming rate • Download capacity unconstrained FMN 2008

9. Data propagation • At time-slot i, root node forwards packet i to m randomly chosen peers • Each peer forwards one packet to one of its neighbors at each time-slot based on the algorithm used • Buffer map exchanges among neighboring peers occur at every time-slot • Forwarding decision based on perfect knowledge • After B time-slots, peers start playing out the content they have received • Buffer size = Playback delay FMN 2008

10. Model skeleton • Transmission trees are different for each packet • The path that a packet follows depends on the local decisions at the peers • Peers having a large amount of neighbors generate per packet distribution trees that are very different • The position of the peers in the distribution trees is statistically the same FMN 2008

11. Model parameters • Number of peers: N • Root capacity: m • Number of neighbors of a peer: d • Buffer size of peers: B • Buffer contents of peer α at time i: FMN 2008

12. Probability that an arbitrary neighbor sends packet j during time-slot i Mathematical model (I) • Denote by Pij the probability that an arbitrary peer is in possession of packet j by the end of time-slot i • Probability that a packet j will be successfully played out • A peer is in possession of a packet at the end of a time slot i, if it already had that packet at time-slot i-1 or if it did not have it but received it by some neighbor during slot i. FMN 2008

13. The factor that differentiates the two considered schemes Mathematical model (II) • We consider an arbitrary peer r that does not have packet j and a neighbor thereof, s, that has it • We define the events • And we get that FMN 2008

14. For small values of d, the dispersion of the measured probabilities around the mean is big whereas as d increases this dispersion becomes smaller and smaller Model validation FMN 2008

15. Playout probability and number of neighbors • Discrepancy between model and simulations for small values of d • For d > 8, the model gives a very good match with the simulations, verifying our assumption of statistical independence • For d > 10, the playout probability seems to be insensitive to the increase of d FMN 2008

16. Playout probability and delay Random Scheduling Minimum delay for optimal tree FMN 2008

17. Playout probability and delay Priority scheduling Minimum delay for optimal tree FMN 2008

18. Scalability • Increase of the minimum playback delay is logarithmic in N for both forwarding schedules FMN 2008

19. Conclusions • We have proposed a general model to study the playback delay in p2p streaming networks • We have proved the validity of the model via simulations • The random forwarding proves to be efficient in delivering data to a large amount of peers at a relatively low delay • Priority scheduling performs poorly even at high playback delays and thus should not be used FMN 2008

20. Playback delay in p2p streaming systems with random packet forwarding Viktoria Fodor and Ilias Chatzidrossos Laboratory for Communication Networks School of Electrical Engineering KTH, Royal Institute of Technology