Hybrid Peer-to-Peer Media Distribution Systems: a

Performance Study

Yicheng Tu, Jianzhong Sun and Sunil Prabhakar

Department of Computer Sciences, Purdue University

Paper published in ACM/SPIE Conference on Multimedia Computing and Networking (MMCN04)

Media Distribution

• Streaming needed• QoS important • Network bandwidth is the bottleneck

– Multicast: CNN.COM– Unicast: online cinema– We concentrate on the latter

• Server-based system lacks sufficient capacity

• Improve capacity by proxies– Contention Distribution Networks (CDNs)

Peer-to-Peer in Media Streaming

• CDNs are expensive to build• Investment increases as popularity of content

does • Peer-to-Peer(P2P) approach:

– The idea: Utilize bandwidth among clients (peers)– Inexpensive– Capacity grows as popularity does

• Problems of P2P systems:– Object searching is slow in pure P2P system (e.g.

Gnutella)– Limited/heterogeneous contributions from peers– Many-to-one streaming, difficult to synchronize – Duration of peer contribution (Peer failure)

Hybrid System = CDN + P2P

• Combine the advantages of both CDN and P2P• Increase of bandwidth by a P2P community• Search is done by a centralized directory server

– Assume object updating is of reasonable frequency

• A small number of seed servers:– Used for streaming– Boot up the system– Complementary bandwidth source in case of failure

• System model and failure-resistant streaming protocol proposed by Xu et al. (2002) and Heefeda et al.(2003)

This Research

• Our Goal: To study the system dynamics of the aforementioned hybrid media streaming system

• Our approach: mathematical analysis – Non-trivial, a good model is the key– Previous attempt (Xu et al., 2002) gives no

analytical results– Confirm analysis by large-scale simulation

System Model • Players:

– Directory Server– Servers

• Same name: Streaming servers, CDN servers

– Peers (clients)• Requesting peer• Supplying peer• Qualified peer

– Media objects• Operations• Order of streaming

entities: peers > servers

(Initial) Assumptions

• Only one object in the system and they are of the same streaming length (L) and bitrate(b) *

• The server side upload link is always the bottleneck

• Peer has infinite storage *• Peer never fails *• Requests are uniformly distributed among

the peer population

Metrics

• System capacity:– total bandwidth of servers + qualified peers

• Server-peer transition time (k0) ***• Reject rate

Intuitively • System capacity growth analogous to population

growth of a single species in a biological system• Servers and supplying peers give birth to

requesting peers• Each streaming cycle equals a generation• Exponential growth

Mathematically

Note α/b is the Capacity Growth Factor, the above can be transformed into

)()()1( kPb

NkPkP

11)(

k

b

NkP

More on Mono-file System

In a system with requesting rate λ, the condition for server-peer transition is:

We get k0 as:

Lbb

Nk

0

1

b

NLb

N

Lbk

b

1lg

lg)lg(log

)1(0

What About Multi-file Systems?

• Previous framework cannot be applied here directly

• Difficult to model the interactions between per-file proliferation

• Analysis in a rather “indirect" way • View system as a combination of F independent

subsystems with and

• Statistical multiplexing (reality) vs. Sharing Multiplexing (our view)

• Then prove the above “view” is close to reality

NNF

ff

1

F

ff

1

k0 in Multi-file System

• Each subsystem follows previous analysis

• Still it is hard to get k0 for the whole system – System-level k0 depends on distribution of Nf

– Nf is unknown – λf is also unknown, but it doesn’t matter

• Lets forget about the real solution to k0 for a while and think about the optimal solution !!

b

NLbk ff

f

1lg

lg)lg(,0

Optimizing System-level k0

• An observation: k0 is the maximum of all k0,f

– System reaches transition only when all single-file subsystem do

• The optimization:Minimize k0 = max {k0,f} (0≤f≤F )Subject to ,

1

NNF

ff

,1

F

ff

.1lg

lg)lg(,0

b

NLbk ff

f

Optimal Choice of Nf

The above optimization has solution: k0 = k0,1 = k0,2 = … = k0,F

Putting into the k0,f formula:

And for all f, we get:What does this mean?

– The optimal choice of Nf is directly related to λf

– Surprisingly, the optimal k0 can be expressed by the same formula for mono-file system

N

Lb

N

Lb

N

Lb

N

Lb

N

Lb

i

i

F

F

2

2

1

1

NN ff

b

NLbk

1lg

lg)lg(0

To Make the Story Complete

• We proved the system converges to the optimal distribution of server bandwidth (Nf)

• We used confidence intervals to analyze how close the system is to the optimal situation– When bNλf/λ > 10, very close !

• What about the assumption of independence among subsystems– We introduce an "independence coefficient”β– βis close to 1 when the pool size M is big– Good thing: M should be and is big in general

Effects of Peer Failures

• Critical feature of any P2P system, cannot ignore• Relate to the biological model: individuals die• Model failures by assigning a lifespan to each

peer, denoted as a random number X• Assume a survival rate γ • For any streaming period k, γ= Pr { X ≥T(k)+ L | X >T(k)} where T(k) is the starting time for period k.

Effects of Peer Failures

• Generally,γis difficult to get– It changes with age (k)– More specifically, it depends on the age structure

• Previous study (Saroiu et al., 2002)shows that peer lifespan follows an exponential distribution

• Revisit the survival rate,

where s is the average lifespan. • The next steps become easy

LsekTXLkTX )}(|)(Pr{

Effects of Peer Failures

• With a universalγvalue,

• Everything else is the same• The transition time

• Note the Capacity Growth Factor becomesγ(1+α/b)

)()()1( kPb

NkPkP

b

bNLbb

k

1lg

)1()1(lg

0

Experimental Results

Experiments: Effects of α

Effects of λ

Effects of Media Number

Number of Peers by Storage Use

Experiments

k0 (h) 1 2 3 4 β

F = 1 8 10319 0 0 0 1.000

F = 50 8 11844 33 0 0 0.997

F = 100 8 10245 23 0 0 0.998

F = 250 9 12209 54 0 0 0.991

F = 500 11 16694 158 1 0 0.981

F = 1000 13 19260 324 1 0 0.967

Effects of Peer Failure

Conclusions

• The hybrid streaming system follows an exponential growth pattern

• The Capacity Growth Factor affects system performance more than other factors do

• Within some boundary, capacity growth of multi-file and mono-file systems can be described by the same equation

• Peer failures have significant effects on system capacity, it could kill the system

• Quantitative analysis of complex system is hard, but doable in some cases

References

• D. Xu, H-K. Chai, C. Rosenburg and S. Kulkarni. Analysis of a Hybrid Architecture for Cost-Effective Streaming Media Distribution. In Proc. of ACM/SPIE MMCN 2003,January 2003.

• M. Hefeeda,  A. Habib, B. Botev, D. Xu,  B. Bhargava, PROMISE:  Peer-to-Peer Media Streaming  Using CollectCast. In Proc. of  ACM Multimedia 2003, Berkeley, CA,  November 2003

• S. Saroiu, P. K. Gummadi and S. D. Gribble. A Measurement Study of Peer-to-Peer File Sharing Systems. In Proc. of ACM/SPIE MMCN 2002,January 2002.