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 (k 0 ) *** 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

More on Mono-file System In a system with requesting rate λ, the condition for server- peer transition is: We get k 0 as:

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

k 0 in Multi-file System Each subsystem follows previous analysis Still it is hard to get k 0 for the whole system –System-level k 0 depends on distribution of N f –N f is unknown –λ f is also unknown, but it doesn’t matter Lets forget about the real solution to k 0 for a while and think about the optimal solution !!

Optimizing System-level k 0 An observation: k 0 is the maximum of all k 0,f –System reaches transition only when all single-file subsystem do The optimization: Minimize k 0 = max {k 0,f } (0≤f≤F ) Subject to

Optimal Choice of N f The above optimization has solution: k 0 = k 0,1 = k 0,2 = … = k 0,F Putting into the k 0,f formula: And for all f, we get: What does this mean? –The optimal choice of N f is directly related to λ f –Surprisingly, the optimal k 0 can be expressed by the same formula for mono-file system

To Make the Story Complete We proved the system converges to the optimal distribution of server bandwidth (N f ) We used confidence intervals to analyze how close the system is to the optimal situation –When bNλ f /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

Effects of Peer Failures With a universalγvalue, Everything else is the same The transition time Note the Capacity Growth Factor becomesγ(1+α/b)

Experimental Results

Experiments: Effects of α

Effects of λ

Effects of Media Number

Number of Peers by Storage Use Experimentsk 0 (h) 1234β F = F = F = F = F = F =

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 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.