1. Fast, Faster, and Correct Roy Friedman Technion Haifa Israel Based on work and discussions with Vadim Drabkin and Gabi Kliot

2. Talk Overview Some recent experience with probabilistic flooding/gossip in ad-hoc networks Theoretical analysis, resulting in some design guidelines A protocol that follows those guidelines and its performance analysis Implications to P2P Some rules of thumbs for developing efficient gossip protocols

3. Ad-Hoc Networks Devices equipped with omni-directional wireless antennas Can transmit messages to all other nodes within a given transmission range R Transmission disk model By forwarding messages, a multiple-hop network is formed p q p q

4. Transmission Overlap On average, the transmission range of two neighboring nodes is 39% [Tseng et al. 2002] So, how many nodes should rebroadcast a message to ensure broadcast delivery with high probability?

5. Reliability vs. # Transmissions

6. Our Conclusions for MANETs The number of senders in each one-hop neighborhood should be a small constant (w.r.t. the network density) Given the concaved shape of the graph It is best to use probabilistic forwarding up to some point Then boost the reliability using deterministic corrective measures

7. RAPID A protocol that follows these design rules The probability of forwarding a message is min( 1, β / Nr ), where Nr is the number of locally observed neighbors, and β the number from the optimal graph (2.5) We use staggering to reduce collisions If during the staggering one of the neighbors of p retransmits the message, then the retransmission of p is aborted If no neighbor retransmits the message after a longer timeout, then p retransmit it We use periodic deterministic gossiping of message headers A node that discovers that it is missing a message m, asks for m from the gossiper There is also a version that tolerates selfish and malicious behavior Purely random Random/ deterministic Deterministic

8. Rapid Performance: Reliability

9. Rapid Performance: Overhead

10. Rapid Performance

12. What About P2P? Analyzing random gossip using bins and balls (Boris Koldehofe 2002) n nodes/bins m random forwarding of a message/balls The reliability is then

13. The Reliability of Gossip # retransmissions # of non-receivers

14. High Availability 101 Suppose the probability of a simple PC is 0.99 The probability that two PCs will be down at the same time is 1-[(1-0.99)^2]=0.9999 Since a PC is much cheaper than an FT computer, one should use clusters for HA

15. Can we Apply the HA Principles for Gossip? That is, can we use two concurrent cheap/fast probabilistic gossip processes instead of a single heavyweight one? Answer: It depends on our cost model and how truly random the probabilistic process is For example, if the probabilistic process is perfect, and the cost is the number of messages, then the only way to boost the performance is using determinism If the cost vs. reliability function is heavy tailed, then we can also gain from multiple random processes

16. Possible Good Cases Fast probabilistic dissemination, combined with periodic gossip of headers (push+pull) Since headers are shorter than messages, we can win here probabilistically Whenever the probabilistic process is not purely random E.g., suppose the dissemination is made to partial views obtained with an lpbcast like membership mechanism Here two independent processes have a chance to correct the imperfectness of each other

17. Conclusions Probabilistic gossip/flooding is a simple, robust, and effective mechanism to disseminate a message to a large percentage of the nodes Beyond that, in some cases we can boost the reliability by having two concurrent probabilistic processes, but in many cases it does not make sense To obtain very high reliability, it is best to complement the probabilistic process with a deterministic recovery one

18. Open Issues Identifying when it is possible to boost the performance with two independent processes Incorporating biased gossip What kind of deterministic corrective measures can be applied in P2P environments?