Probabilistic Quorum Systems in Wireless Ad Hoc Networks

1. Probabilistic Quorum Systems in Wireless Ad Hoc Networks Gabriel Kliot, Roy Friedman Technion – Israel Institute of Technology and Chen Avin – Ben Gurion University, Israel

2. How Can One Find Data? Centralized directory Flooding lookup requests or advertisements expensive Directory Server Advertise Lookup Data Owner Data Client

3. How Can One Find Data? Publishing advertisements to a subset P and looking up the data in a subset L such that P and L intersect This is known as quorums

4. Quorum System: A set of subsets over a universe U such that for any Q1,Q2 in Q, Q1∩Q2≠Ф Bi-quorum System: A couple of sets of subsets (Q1,Q2) over a universe U such that for any Q1 in Q1and Q2 in Q2, Q1∩Q2≠Ф Quorums and Bi-Quorums Majority

5. Probabilistic Quorums [Malkhi, Reiter, Wool, Wright ‘01] • In probabilistic quorums, the intersection property is only ensured with some probability • The members of the probabilistic quorum are selected on each quorum access using an access strategy • For example, pick nodes at random • This ensures intersection with probability • Suitable for dynamic ad hoc networks

6. Our Contributions • Different accesses strategies, with varying trade-offs • Mix and Match theorem – we can mix them in different ways, that guarantee intersection • Asymmetric bi-quorum systems • Explore various combinations • Theoretically, based on Random Geometric Graph model • By simulations • Along the way, some theoretical results about Random Walks in Random Geometric Graphs

7. Formal Network Model: 2D Random Geometric Graph • n nodes • 2-dimensional unit torus [0,1]2 • Uniform placement • Edge between 2 nodes within Euclidian distance r • No geographic knowledge • We use Random Geometric Graph only for performance analysis • The correctness is ensured on any topology

8. Access Strategies in MANET RANDOM Early halting (if accessed serially)‏ Membership / sampling service Routing PATH (RW)‏ No routing Early halting Revising nodes along the path High Crossing Time Partial Cover Time Depends on TTL(no fine grained control over the cost)‏ FLOODING No routing No Early halting Multiple replies MAC broadcast: • Not EE • Low bandwidth Access Cost (Random Geometric Graph)‏ Good Bad Ugly

9. Mix and Match Known result [Malkhi, Reiter, Wool, Wright]: If two quorums of size are chosen uniformly at random, then their non-intersection probability is Our result: We show that if one of these quorums is chosen uniformly at random, then the other quorum can be chosen in any way (including deterministically)‏

10. Mix and Match Specifically, assume Qa and Qb, Qa chosen uniformly at random and Qb chosen arbitrarily, but in a non-adversarial manner (e.g., using the PATH access strategy)‏ Lemma 1: Lemma 2: In order to have intersection with probability 1-ε, the sizes of Qa and Qb must satisfy For example, for an intersection probability of 0.9, we can pick

11. Optimized RANDOM strategy Adding Cross Layer Optimization Similar to RANDOM, except that a lookup request that passes through any intermediate node does a local lookup as well Benefit comes from the mix&match result That is, as soon as the first lookups visit nodes, it is likely that the object will be found Typically, after picking only a few nodes to visit

12. Optimized PATH strategy - Unique PATH By remembering the path, we can avoid revisiting nodes and speed up the walk

13. Comparing the Access Strategies Comparing the Access Strategies

14. Simulation setup Simulations on JIST/SWANS http://jist.ece.cornell.edu/ Network sizes: 50, 100, 200, 400, 800 Random Waypoint mobility model Speed between 0.5-2 m/s (walking speed)‏ Average pause time 30 s Transmission range ~220m Average number of neighbours davg=10 10 runs per data point, 1000 sec

15. Simulations Scenarios 100 advertisements to a RANDOM quorum of size nodes 1000 lookups 4 strategies: RANDOM, RANDOM-OPT, UNIQUE-PATH, and FLOODING On a hit, a reply was sent to the originator Each hop is counted as one message Hit ratio means the number of successful lookups for objects that were published Corresponds to intersection probability

16. Results of RANDOM and RANDOM-OPT Theory works… A hit ratio of 0.9 was obtained with a quorum size of With 800 nodes, the quorum size is 33 The number of messages per lookup behaved as RANDOM RANDOM-OPT But, the overall communication cost was greatly affected by routing overhead, even in RANDOM-OPT

17. # Lookup Messages for RANDOM-OPT Mobile network

18. Total # Messages for RANDOM-OPT This includes the cost of routing in a mobile network

19. Hit Ratio for UNIQUE-PATH • Mobile network For N=400, |lookup _Q|=23~1.15*sqrt(400)‏ guarantees intersection of 0.9 – like in theory

20. # Lookup Messages for UNIQUE-PATH No routing overhead here! Number of messages is smaller than quorum size! Due to early halting.

21. Hit Ratio for FLOODING

22. # Lookup Messages for Flooding No routing overhead here too

23. Simulation summary RANDOM_OPT UNIQUE-PATH FLOODING static 35 (140 with routing)‏ 14 15* mobile 50 (600 with routing)‏ 14 15* • 400 nodes • #lookup msgs that guarantee 0.9 intersection • Including reply • Flooding is sent by broadcast • Hidden overheads • Flooding does not allow fine grained control • If we want to increase the intersection probability, we must increase TTL, which will increase the #msgs significantly

24. Conclusions Examined various combinations of access strategies for probabilistic quorums in MANETs RANDOM RANDOM-OPT PATH UNIQUE-PATH FLOODING Showed that it is possible to obtain efficient probabilistic quorums In particular using asymmetric combinations Using Random walks More about handling failures and dynamism in the paper

25. Future Directions Shared objects (with linearizable semantics)‏ Pub/sub Distributed search

26. Q&A Contact: Gabriel Kliot gabik@cs.technion.ac.il Thank You !