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

Outline  Introduction  Related Work  Proposed Method  Simulation  Conclusion

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

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.

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.

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

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

Example Node ix ≡ 1 (mod 3) Node jx ≡ 2 (mod 5) prime Starting counting period

Chinese Remainder Theorem if x 0 is one such solution, then an integer x satisfies the congruences if and only if x is of the form x = x 0 + km for some integer k. One x 0 is: The goal is to find an x such that c i |m i and c j |m j. We can express this as a pair of simultaneous congruences There is exactly one such overlapping period every m = mimj periods. Letting x represent the reference period number, we have where the solution is unique (mod m) for m = m i m j, and where b i and b j must satisfy the congruences

Duty cycle Duty Cycle (DC) = 1/m i Node ix ≡ 1 (mod 3) Node jx ≡ 2 (mod 5) DC = 1/3 =33% DC = 1/5 =20%

Coprimes are not enough  The moduli cannot be chosen independently by the nodes Such choices could lead to values of m i and m j 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 m i = m j, then node i and j may never discover each if they wake up with the same period but different phase.

Example x cici cjcj Node ix ≡ 1 (mod 3) Node jx ≡ 2 (mod 3)

Coprimes are not enough (cont.)  To require each node i to pick two primes, p i 1 and p i 2, such that p i 1 ≠ p i 2 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 {(p i 1, p j 1 ), (p i 1, p j 2 ), (p i 2, p j 1 ), (p i 2, p j 2 )} that are relatively prime ex: (p i 1, p i 2 ) = (30, 77) and (p j 1, p j 2 ) = (35, 66) x = 30k and x = 77k, for all k ∈ Z + x = 35k + 1 and x = 66k + 1, for all k ∈ Z +

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 = × 97 = 5141

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.

Duty Cycle form Discovery Latency Maximum discovery latency: t disco, Without loss of generality, p = p i 1 = p j 1 The minimum duty cycle, DC, must satisfy the following inequality The minimum required beacon rate:

Simulation Study Programming languagenesC Operating SystemTinyOS Empirical Sensor NodeTelos Wiress sensor node

Discover Latency Comparison

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

Impact of Duty Cycle Asymmetry

Latency-Driven Discovery

Empirical Evaluation

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.

Thank you