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

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1 3

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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

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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

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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

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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

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)|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

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Playout probability and delay

Minimum delay for optimal tree

Random Scheduling

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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