Practical Asynchronous Neighbor Discovery and Rendezvous for Mobile Sensing Applications

Prabal Dutta and David culler 6th ACM conference on Embedded network sensor systems (2008)

Jihee Ryu , Keunchan Park, Jaehyun Han, and Kihoon Cha

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Contents Introduction Problems & Solution Approach Related Work Simplified Algorithm Disco Example Design

Why two primes are chosen? Pair of Primes Slot non-alignment To Avoid Choosing The Same Pair

Discussion Pros & Cons

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Introduction

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Mobile object interacts with other mobile and static objects 3 common patterns – talking, docking, and flocking

Neighbor Discovery A sensor node discovering another (one-hop) sensor node

Rendezvous Delivering messages to previously discovered neighbors

Talking Docking Flocking

Introduction(cont’)

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Characteristics of Sensor Network Nodes may have different capabilities

Energy Functionality Mobility

Nodes operate at different (asymmetric) duty cy-cle Duty Cycle (DC): The fraction of time that a system is in

an "active" state Nodes starts asynchronously

No synchronization

Problems & Solution Approach

Problems Approaches

- Energy consumption - Low duty cycle (e.g. 1%)

- Link Dynamics (to de-tect addition of new links or attrition of old links)

- Asynchronous neigh-bor discovery based on Chinese Remainder Theorem

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Related work

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T

LR

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m

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• Birthday [McGlynn01]• Randomly choose to listen,

transmit or be idle (sleep)• Unpredictable

• Quorum [Tseng02]• Listen during a row • Transmit during a column• Global agreement on duty

cycle

Two nodes, i and j reference period number, x start their counters ci and cj at arbitrary times, say x = 1 and x = 2 increment counters with equal period Tslot and wake up at some relatively prime intervals, say mi = 3 and mj = 5

Dark cells indicate times when node i and j turn on radios Both nodes are awake at times x = 7 and x = 22

x = 7+15k, k Z+

Disco uses two primes/node to ensure pair-wise relative primes

Simplified algorithm

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Disco Example

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Node i is awake at times: 5, 10, 15, 20, 25, 30, 25, and 7, 14, 21, 28, 35,…

Node j is awake at times: 1, 6, 11, 16, 21, 26, 31, and 1, 8, 15, 22, 29, 36, …

Nodes i and j are both awake at: 15, 22

Two primes per node ensures even if both nodes pick same primes, dis-covery will occur

1 2 3 4 5 67 8 9 10 11 12

13 14 15 16 17 1819 20 21 22 23 2425 26 27 28 29 3031 32 33 34 35 36

Why two primes are chosen?

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The prime cannot be chosen independently by the nodes

Restriction of the coprimes to expression their de-sired duty cycle (1, ½, 1/3, … 1/k, where k Z+)

If prime of node i equals prime of node j, then nodes i and j may never discover each other if they wake up with the same period but different phase

Pair of Primes

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To Overcome Previous Limits Choosing two primes, p1 and p2

Such that p1 ≠ p2 and the sum of their reciprocals (ap-proximately) equals the desired duty cycle

Simple Validation Ensuring a coprime pair from any two nodes

A coprime pair is exist in the set of probable pairsE.g. node i picks (3, 5) and node j picks (5, 7) {3,5} / {3,7} / {5,5} / {5,7} 3 rendezvous casesE.g. node i picks (30, 77) and node j picks (35, 66) {30,35} / {30,66} / {77,35} / {77,66} 0 rendezvous cases

Slot non-alignment In practice, slots will rarely be aligned because nodes

are… run independently do not adjust clock skews

To discover other node, transmits a beacon at both the beginning and end of a slot when

beaconing

Node i

Node j

Slot

Beacon

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Node i

Node j

To Avoid Choosing The Same Pair

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Assumption There are classes which do not need to discover each

other Deterministic algorithm

An ordered list of possible prime pairs are generated A prime pair’s position indicate a particular class’s modulo

Example Target duty cycle = 1%, Number of classes = 3

(101,10103) (103,3433) (107,1523) (109,1201) (113,863) …

Class 1 Class 2 Class 3 Class 1 Class 2 …

Glossary Balanced primes

the intra-node primes are approximately equal (e.g.37 and 43). Unbalanced primes

the intra-node primes are significantly different (e.g.23 and 157). Symmetric pairs

both nodes choose the identical pair of primes Asymmetric pairs

both nodes choose a different pair of primes

Discovery Latency the delay between the moment two nodes are within communi-

cations range to the moment when they first discover each other

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Implementation t_slot = 10 ms

An Application can control Parameters

Ex) DC

The beaconing pol-icy Listening Beaconing

Power

Beacon

Slot

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Beacon Rate Adaptation By the implementation, beacon mode can be

changed

Sending beacons during their normally sched-uled rendezvous slots with nodes in their neighbor table to ensure that routing links remain connected and synchronized, but they would not send other beacons

Sharing neighbors information, new node can discover neighbor more faster than expected

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Impact of Duty Cycle Asymmetry

Suggests that more powerful beacons combined with less powerful mobile tags is feasible and beneficial

Static(High DC)

Mobile(Low DC)Mobile(Low DC)Mobile(Low DC)

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Predictable

2%

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Robustness to Clock Skew Over longer timescales, nodes that have sig-

nificantly different skews are likely to have difficulty with rendezvous

but asynchronous discovery should still work

Node i

Node j

Node k

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Pros

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Algorithm is simple A solution to the low-power asynchronous

neighbor discovery problem in mobile sensing applications

It is possible to make decision independently at node sides

Cons

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Why they use a slot numbers at evaluation? Different discovery time for different nodes Restriction of possible number of frequency

Discovery Rate

Small time slot makes neighbor discovery faster21

Why they use a slot numbers at evaluation?

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Different discovery time for different nodes

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29, 67

23, 157

29, 67

23, 157

Restriction of possible number of fre-quency

1% duty cycle : 21 pairs 5% duty cycle : 4 pairs

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