1 / 28

On the Stability and Optimality of Universal Swarms

On the Stability and Optimality of Universal Swarms. Xia Zhou*, Stratis Ioannidis ♯ , and Laurent Massoulié + * University of California, Santa Barbara ♯ Technicolor Research Lab, Palo Alto + Technicolor Research Lab, Paris. Bit-Torrent Swarms.

vianca
Download Presentation

On the Stability and Optimality of Universal Swarms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. On the Stability and Optimality of Universal Swarms • Xia Zhou*, Stratis Ioannidis♯, and Laurent Massoulié+ • *University of California, Santa Barbara • ♯Technicolor Research Lab, Palo Alto • +Technicolor Research Lab, Paris

  2. Bit-Torrent Swarms • Swarm: set of users interested in the same file • Seed

  3. Bandwidth Under-Utilization • Online P2P Networks • [Hajek and Zhu 10] • Unstable when λ> s! • Missing-piece syndrome: Each peer waiting for only onepiece • Seed • s chunks per sec • λ peers per sec

  4. Bandwidth Under-Utilization • Mobile P2P Networks • Cached content is shared in a P2P fashion (eg. bluetooth) • Opportunistic communication • May not encounter the content they are interested in • ?

  5. Universal Swarms • Key idea: Exchange chunks across swarms upon bandwidth under-utilization • Question 1: How does such inter-swarm exchange affect stability? • Question 2: How should items be exchanged among swarms?

  6. Our Contributions • A versatile modelfor universal swarms • Universal swarms achieve better stability compared to autonomous swarms • Only one swarm can become unstable! • Optimal replication ratios that minimize the time for peers to retrieve interested content

  7. Outline • Motivation • A model for universal swarms • Main results • Stability of universal swarms • Content exchange designs in universal swarms • Conclusion and future works

  8. Peer Swarms • Peer requests one chunk iK • Peers requesting the same chunk form a peer swarm • ? • ? • ?

  9. Peer Caches • Peer has cache size of C • Peer may use cache to store chunks it is not interested in • Cache • Request • C • ? • Stored chunks fK

  10. Peer Arrivals • Peers arrive with full caches • Peers requesting iandcaching f arrive according to a Poisson process with rate λi, f • Cache • Request • C • ? • ? • ? • ? • Time

  11. Peer Contact Process • Online P2P: random sampling • Mobile P2P: contact when within transmission range • × • × • Time • ? • ? • ?

  12. Peer Contact Process (Cont.) • One peer contacts other peers according to a Poisson process with rate • N(t): number of peers in the system at time t • 0 ≤ β < 1 • β = 1 • 1< β ≤ 2 • Contact rate • Contact rate • Contact rate • μ • Contact-constrained • Constant-bandwidth • Interference-constrained • N(t) • N(t) • N(t)

  13. Content Exchange Policy • If encountering requested chunk: Grab-and-Go • Otherwise: • Static-cache policy: no change on cached chunks • Alternatives: updating cached contents • Requested chunk and cached chunks define a peer class • N(t): system state at time t (# of peers in each peer class) • A, A’  B, B’ • Conversion probability • ? • ? • ?

  14. Outline • Motivation • Model for universal swarms • Main results • Stability of universal swarms • Content exchange designs in universal swarms • Conclusion and future works

  15. Methodology: Fluid Limit • The evolution of the universal swarm system can be approximated arbitrarily well by the solution of a system of ODEs that depend on the conversion probabilities • For allβ • For all content exchange policies

  16. Universal Swarms • Question 1: How does inter-swarm exchange affect the system stability?

  17. Stability of Static-Cache Policy • Let > 0 be the arrival rate of peers requesting i and storing j. Theorem: The system is stable under the static cache policy if and only if: • Independent of β and cache size C • The system is stable even if arrivals of peers requesting i exceed arrivals of peers storing i! 16

  18. Only One Swarm Can Become Unstable! • ? • ? • ? • At most one swarm can blow up!

  19. Outline • Motivation • Model for universal swarms • Main results • Stability of universal swarms • Content exchange designs in universal swarms • Conclusion and future works

  20. Universal Swarms • Question 2: How should chunks be exchanged across swarms?

  21. Optimal Demand and Supply • -- the number of peers requesting chunk i (demand) • -- the number of peers storing chunk i(supply) Theorem: Under the grab-and-go principle, the average sojourn time of a peer in the system is minimized when where . • The optimal supply is C times the demand!

  22. BARON: Valuation-Guided Replication • Centralized tracker maintains valuation vi for each chunk i • Positivevi: chunk i needs more replicas • Negativevi: chunk i needs fewer replicas • Replace the chunks with negative valuation with that with positive valuations 2 1 0 -1 … • ? • ?

  23. BARON: Valuation Design • -- the number of peers requesting chunk i in the optimal state • -- the number of peers storing chunk iin the optimal state Optimal: Valuation: • No need to know arrival rates and contact rates, but only the cache size C •  Need to track the demand and supply dynamically

  24. BARON: Numerical Results • Evaluations based on fluid trajectories in MATLAB • Numerically solving ODEs • Valuation-guided content exchange improves the system stability

  25. Conclusion and Future Works • Universal swarms achieve better stabilityeven with the simplest replication strategy • At most one swarm can blow up! • Optimal supply linearly proportional to the demand • BARON extends the stability region using valuations • Better understanding of the dynamics under more sophisticated content exchange mechanisms • Peer incentives • Removing the assumption of one-chunk request

  26. Thank you!

  27. Backup

  28. Only One Swarm Can Become Unstable! • Let > 0 be the arrival rate of peers requesting i and storing j. Theorem: There exists at most one item ifor which Moreover, for β in [0,1], the number of peers requesting item igrows to infinity, while the number of peers requesting other items remains bounded. • At most one swarm can blow up!

More Related