Playback delay in p2p streaming s ystems with random packet forwarding
description
Transcript of Playback delay in p2p streaming s ystems with random packet forwarding
Playback delay in p2p streaming systems with random packet forwarding
Viktoria Fodor and Ilias Chatzidrossos
Laboratory for Communication NetworksSchool of Electrical EngineeringKTH, Royal Institute of Technology
18-Sep-08 FMN 2008 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
18-Sep-08 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
18-Sep-08 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
S
3
9
1
7
2
5
6
84
S
645
927 8
1 3
S
3
9
1
7
2
5
6
84
S
645
87
1 3
2 9
18-Sep-08 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
sr
3 64 3 76545
sr
3 64 3 7654Req. 5
5
How do peers know whether some of their neighbors have a specific packet or not?
18-Sep-08 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
15 2120191716 24
1 1011 1 1001
B(1) = 15
B(10)= 24
…
18-Sep-08 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
j-2 j+1br
j-2 j+2j+1jj-1bs
pick randomly one of them
j-2 j+1
j-2 j+2j+1jj-1
br
bs
18-Sep-08 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
18-Sep-08 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
18-Sep-08 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
18-Sep-08 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:
iB
18-Sep-08 FMN 2008 12
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.
Probability that an arbitrary neighbor
sends packet j during time-slot i
jBjpl PP 1
18-Sep-08 FMN 2008 13
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
)Pr(),|Pr(
)|Pr(si
si
ri
ri
ji
BjBjBjrtojpacketsendss
Bjrtojpacketsendss
}{:
}{:
}{:
rtosendtochosenhasitthatgivenjpacketsendtochoosessD
rtosendtochoosessC
ithavenotdoesrandjpackethassA
)|()|()|( ADPACPArtojpacketsendssP
The factor that differentiates the two considered schemes
18-Sep-08 FMN 2008 14
Model validation
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
18-Sep-08 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
18-Sep-08 FMN 2008 16
Playout probability and delay
Minimum delay for optimal tree
Random Scheduling
18-Sep-08 FMN 2008 17
Playout probability and delayPriority scheduling
Minimum delay for optimal tree
18-Sep-08 FMN 2008 18
Scalability
Increase of the minimum playback delay is logarithmic in N for both forwarding schedules
18-Sep-08 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
Playback delay in p2p streaming systems with random packet forwarding
Viktoria Fodor and Ilias Chatzidrossos
Laboratory for Communication NetworksSchool of Electrical EngineeringKTH, Royal Institute of Technology