Practical Asynchronous Neighbor Discoveryand Rendezvous for Mobile Sensing

Applications

Prabal Dutta and David CullerComputer 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-comple

te 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, mi and mj , such that mi and mj are relatively prime (coprimes)

Example

Node i x ≡ 1 (mod 3)

Node j x ≡ 2 (mod 5)

prime

Starting counting period

Duty cycle

Duty Cycle (DC) = 1/mi

Node i x ≡ 1 (mod 3)

Node j x ≡ 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 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 c

ycle 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.

Example

x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

ci - - 0 1 2 3 4 5 6 7 8 9 10 11 12 13

cj - 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Node i x ≡ 1 (mod 3)

Node j x ≡ 2 (mod 3)

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∈ +

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 = 9094953 × 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: tdisco,

Without loss of generality, p = pi1 = pj1

The minimum duty cycle, DC, must satisfy the following inequality

The minimum required beacon rate:

Simulation Study

Programming language nesC

Operating System TinyOS

Empirical Sensor Node Telos 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

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