Practical Asynchronous Neighbor Discovery and Rendezvous for Mobile Sensing Applications

1. Practical Asynchronous Neighbor Discoveryand Rendezvous for Mobile Sensing Applications Prabal Dutta and David Culler Computer Science Division University of California, Berkeley ACM SenSys 2008

2. Outline • Introduction • Related Work • Proposed Method • Simulation • Conclusion

3. Introduction • Challenge for asynchronous neighbor discovery: • Awake infrequently • Co-located discover each other • Without any prior knowledge of their potential encounters • Without external assistance

4. Introduction • Two requirements • Low-power operation • Active vigilance • These are at odds with each other since optimizing for one may come at the expense of the other.

5. Related Work • Prior Work in asynchronous neighbor discovery: • Stochastic • McGlynn and Borbash proposed “Birthday Protocols” • Quorum • Tseng et al. propose a quorum-based protocol for multihop ad hoc networks • Combinatorial • For asymmetric duty cycles, the approach reduces to an NP-complete minimum vertex cover problem requiring a centralized solution.

6. Goal • Discovery can be quite valuable in mobile networks • Discovery should be a fundamental and continuous service in both mobile and static networks • “Disco” addresses a more general set of neighbor discovery problems and avoids the need for a randomized protocol by using pairs of primes

7. Proposed method –using Chinese Remainder Theorem Two nodes, i and j, pick two numbers, mi and mj , such that mi and mj are relatively prime (coprimes) Choosing a prime Starting counting at reference period

8. Example prime Node i x ≡ 1 (mod 3) Node j x ≡ 2 (mod 5) Starting counting period

9. Duty cycle Duty Cycle (DC) = 1/mi Node i x ≡ 1 (mod 3) DC = 1/3 =33% Node j x ≡ 2 (mod 5) DC = 1/5 =20%

10. Coprimes are not enough • The moduli cannot be chosen independently by the nodes • Such choices could lead to values of mi and mj that are not coprimes. • Restricting the moduli to coprimes is not scalable • There are only a handful numbers that can satisfy both the target duty cycle and coprime requirement. • If mi = mj, then node i and j may never discover each if they wake up with the same period but different phase.

11. Example Node i x ≡ 1 (mod 3) Node j x ≡ 2 (mod 3)

12. Coprimes are not enough (cont.) • To require each node i to pick two primes, pi1 and pi2, such that pi1≠ pi2 ex: Duty Cycles are 97 and 103 (1/97 + 1/103 = 2%) • For every pair of nodes i and j, there will be at least one pair in the set {(pi1 , pj1 ), (pi1 , pj2 ), (pi2 , pj1 ), (pi2 , pj2 )} that are relatively prime • ex: (pi1 , pi2 ) = (30, 77) and (pj1 , pj2 ) = (35, 66) • x = 30k and x = 77k, for all k ∈ Z + • x = 35k + 1 and x = 66k + 1, for all k ∈ Z+

13. Choosing Primes • Low discovery times are possible: • one of the primes is very close to the reciprocal of the duty cycle • the other prime is a much larger number • The limit of the ratio between the auspicious and unfortunate worst-case latencies is Node i : (53, 883) Node j : (97, 103) 883 × 103 = 90949 53 × 97 = 5141

14. Slot Non-Alignment • To maximize the likelihood that overlapping slots result in discovery, Disco transmits a beacon at both the beginning and end of a slot.

15. Duty Cycle form Discovery Latency Maximum discovery latency: tdisco, Without loss of generality, p = pi1 = pj1 The minimum duty cycle, DC, must satisfy the following inequality The minimum required beacon rate:

16. Simulation Study

17. Discover Latency Comparison

18. Discovery Latency: A Deeper Look prime pairs: (23,157), (29, 67), (31, 59), (37, 34)

19. Impact of Duty Cycle Asymmetry

20. Empirical Evaluation

21. Conclusion • This paper presents a practical solution to the low-power asynchronous neighbor discovery problem. • This simple protocol achieves discovery faster than other discovery protocols for a given duty cycle, allows nodes to independently select their own duty cycle.

22. Thank you