An Analytical Study of Low Delay Multi-tree-based Overlay Multicast György Dán and Viktória Fodor...

An Analytical Study of Low Delay Multi-tree-based Overlay Multicast

György Dán and Viktória Fodor

School of Electrical EngineeringKTH, Royal Institute of Technology

Stockholm, Sweden

Peer-to-Peer Streaming and IP-TV Workshop

http://www.ee.kth.se/~gyuri

Motivation Live peer-to-peer streaming Many proposed systems

Push-based vs. Pull-based Tree-based vs. mesh-based vs. unstructured

Multi-hop data delivery Failures – node departures, packet losses Delivery time hard to predict

Playback delay and playout buffer dimensioning


Does playback delay matter? Designer’s goal:

Control the playback delay (minimize?)

Our goal:Identify sources of delay


A packet’s eye view of the overlay Four components of delay: Dd=Dp+Dtr,o+Dpr+Dtr,i

(a: pkt size, Cin: input bandwidth, Cout: output bandwidth)

R

A spanning tree of the overlay traversed by a packet

Dpr

Dtr,i=Win +a/Cin

Dp

Dtr,o =Wout +a/CoutDd

Tree properties depend on

Tree-based:Overlay maintenance

Unstructured:Scheduling algorithm


One-hop propagation model Possession-propagation-reception

Dd

1

1

Layer l-1

Layer l

h

)(1, hflj

Possession probability

)(hfd

h

Per-hop delay

Reception probability

h

)(, hlj


One-hop propagation model Possession-propagation-reception

Dd

h

)(1, hflj

1

h

)(, hlj1

Layer l-1

Layer l

)(hfd

h

Possession probability

Per-hop delay

Reception probability


Multi-hop propagation model Without FEC

Apply the one hop model to every layer

Result is the convolution of the per-hop delays

R

With FEC Apply the one hop model to

every layer Calculate the result iteratively

h

d

fljlj dfh

h

h

h

0

1,, )()()(


Multi-hop propagation model Probability of reception by time h in layer l for packet j

Probability of possession by time h in layer l for packet j

Source node – initial condition

Numerical solution Converges Scalable

h

d

fljlj dfh

h

h

h

0

1,, )()()(

k)(h)R(h))P(-(1(h) (h)ji

li,lj,lj,lj, i

f

(h)fj,0

A control theoretic interpretation: Dynamical system with Input signal Output signals

(h)fj,0

(h)flj,


Multi-hop propagation model Probability of possession with playback delay b

(playout deadline of packet j: hj=b+(j−1)a/B)

Probability of possession for arbitrary node and packet

Inputs of the model Initial condition Nl number of nodes in layer l Fd(h) node-to-node delay distribution

k))(hR))P((h-(1)(h (b) jji

li,jlj,jlj,lj, i

n

j

L

lllj Nb

Nnb

1 1, )(

11)(

- Source playout strategy

- Overlay structure

- Scheduling, structure


Application – Multi-tree overlay Source and N nodes Source capacity > m*B t trees, each node forwards in d trees Retransmissions and FEC(n,k) for error control Packets sent at round-robin from the source

R1

5 86 2 39

741

R3

1 87 2 54

396

R2

1 76 4 39

825

Tree 2Tree 3Tree 1

P1 P2 P3

1)a/B)-(j-H(h (h)fj,0

h

)(0, hfj

1

j=1 j=2 j=3

Initial condition


Overlay structure Number of nodes per layer (Nl)

Calculated recursively based on Node output capacity distribution Prioritization scheme Capacity allocation scheme

Prioritization schemes Contribution based

Contributors prioritized over non-contributors (NP) Priority proportional to potential contribution (P)

Capacity allocation schemes In case of excess capacity

Proportional contribution (MM) Non-proportional contribution (FU)

)1(

l / NlRr

r d

)),//(min( N1 mdtN


Node-to-node Delay Input link

Dtr,i=Win+a/Cin

Win waiting time of a packet in a G/D/1 queue

Output link Dtr,o =Wout +uIdat/(rB),

where I[1, r/d] d.r.v Wout waiting time as seen by an arriving

batch of r/d packets in a GIX/D/1 queue

Retransmissions Loss detection, etc

Arrival processes What is a realistic model?

1)(lim

hFdh

h

)(hfd


Model validation Discrete event driven simulator

Steady state Media server on a 10Mbps-20Mbps link (m=50) Low bitrate media, B=112kbps Nodes buffer 15s worth of packets Input and output capacity constraints Propagation delays

Random network topology – GT-ITM

Node churn for randomness Results shown for packet losses


Deterministic arrival process

Inf.cap.Cin = Cout = 10 Mbps

Inf.incap.Cin =10 MbpsCout=128 kbps

Fin.cap.Cin = Cout = 128kbps

Number of trees influences the delay – is there an optimal number?

Dpr plays a minor role – but increasing importance

N=104,p=0.1


Poisson arrival process

Inf.cap.Cin=Cout=10Mbps

Inf.incap.Cin=10MbpsCout=128kbps

Fin.cap.Cin=Cout=128kbps

Queuing delay significant

Decrease utilization

N=104,p=0.1


Simulation Inf.incap.

Cin=10 MbpsCout=128 kbps

Fin.cap.Cin=Cout=128 kbps

Similar to deterministic arrival process

N=104,p=0.1


FEC and retransmissions Dynamically

adjust playback delay

FEC cannot achieve (b)=1

But FEC can help to keep the playback delay low

Scalability?


Capacity allocation and prioritization

Scen. Share Cout

[kbps]CH 100% 256

CI65% 12835% 512

Prioritization and uneven capacity allocation best: increases the average output capacity of the contributing nodes

Inhomogeneous upload capacity can help to achieve better performance

Capacity allocation MM: proportional FU: non-proportional

Prioritization NP: contributor/non-

contributor P: proportional to

contribution

FU+P

MM+P

N=104


Conclusion Main factors that determine the delay

Average upload capacity of contributing nodes Waiting times in queues at the nodes

The ways to decrease the end-to-end delay are decreasing the number of layers (by prioritization), FU allocation,

and by increasing m as much as possible – no fairness...

using an adequate number of trees (though using a few trees only might imperil the stability of the overlay for given n, k, p)

dynamically adjusting the FEC redundancy

using a bitrate not too close to E[Cout]


Open questions Application to pull-based systems

Modeling tree structure and delay distributions

Scalability in terms of delay

Optimal chunk size and out-degree Easy to control in multi-tree-based overlays (?)

How to control in a pull based overlay?

An Analytical Study of Low Delay Multi-tree-based Overlay Multicast

György Dán and Viktória Fodor

School of Electrical EngineeringKTH, Royal Institute of Technology

Stockholm, Sweden

Peer-to-Peer Streaming and IP-TV Workshop

An Analytical Study of Low Delay Multi-tree-based Overlay Multicast György Dán and Viktória Fodor...

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