Deterministic Recurrent Communication and Synchronization in...

Deterministic Recurrent Communication andSynchronization in Restricted Sensor Networks

A. Fernandez Anta M. A. Mosteiro Christopher Thraves

ASAP Research teamIRISA/INRIA Rennes

ALGOSENSORS 2010

A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization1/25

1 Introduction

2 Model and Problem Definition

3 Our Solution

4 Open Problems

Introduction

A sensor node

Capabilities

processing

sensing

communication

Limitations

memory

life cycle

University of California, Berkeley and

Intel Berkeley Research Lab.

PicoBeacon

Berkeley Wireless Research Center

Introduction

A sensor node

Capabilities

processing

sensing

communication

Limitations

memory

life cycle

Introduction

A sensor node

Capabilities

processing

sensing

communication

Limitations

memory

life cycle

Introduction

A sensor node

Capabilities

processing

sensing

communication

Limitations

memory

life cycle

Introduction

A sensor node

Capabilities

processing

sensing

communication

Limitations

memory

life cycle

Introduction

A sensor node

Capabilities

processing

sensing

communication

Limitations

memory

life cycle

Model and Problem Definition

Network and Nodes

Deployed at random in the area of interest.

Unique identification number (ID) in 0, 1, 2, . . . , n − 1.

Limited communication range (transmission = reception)

⇒ nodes can duplicate their communication range.

n, k and D are known by all the nodes in the system.

Network and Nodes

Network model: Geometric Graph

Local Synchrony

Time is assumed to be slotted (steps).

Each transmission occurs in a given slot.

The slots of all nodes are in phase.

Availability of a hardware clock mechanism: local-clock.

Local Synchrony

Node Reliability

Nodes may fail, BUT:

⇒ the network stays connected (one connected component) at alltimes

⇒ the first node awakened is always awake

⇒ each period when a node runs without failures lasts at least thelength of the stabilization time.

Node Reliability

Node Awakening

Definition

A τ -adversary is an adversary that awakens all the nodes of the networkwithin a window time of size τ , i.e., no node is awakened at a time t ≥ τ .Additionally, a τ -adversary does not recover crashed nodes. The parameter τis assumed known by the nodes.

Definition

An ∞-adversary is an adversary that has no restriction on when nodes areawakened.

DRC Problem

Definition

A distributed protocol solves the deterministic recurrent communication

(DRC) problem if it guarantees that, for every step t and every pair(u, v) ∈ E, there is some step t′ ≥ t such that, in step t′, v receives anapplication message from u.

Why Deterministic Communication?

Only one channel of communication

⇒ must deal with collision of transmissions!

Popular solution → random protocols.

BUT scarcest resource is energy and

random protocols ⇒ redundant transmissions!.

⇒ deterministic protocols may help.

Motivation and Evaluation

Sensor Networks application: monitor physical phenomena.

⇒ protocols must guarantee communication infinitely many times.

Optimization criteria:

1) low energy cost.

2) short delay between transmissions.

1) low energy cost.

Related Work

Message passing:

[ABLP’92] Each node receives from all neighbors inO(k2 log2 n/ log(k log n)). → synchronous start. ω(1)-degreebipartite-graphs requiring Ω(k log k). → not embeddable in GG.

Broadcast & gossiping:

[CGR’00, CGOR’00, CR’03, CGGPR’02] → synchronous start, globalclock, etc.

Selection

[Kowalski’05] Static, ∃O(k log(n/k)), +[I’02]: O(k polylog n). →synchronous start. Dynamic O(k2 log n). → nodes turn off upon succ.transmission.

Selective families:

[I’02] ∃(k, n)-selective families of size O(k polylog n).[DR’83] (m, k, n)-selectors must be Ω(minn, k2 log

kn) when m = k.

[DBGV’03] (k, k, n)-selectors must be ≥ (k − 1)2 log n/(4 log(k − 1) + O(1))and ∃(k, k, n)-selectors of size O(k2 ln(n/k)).All → synchronous start.

Our Solution

The Algorithm

We design our protocols assuming the existence of an oblivious

deterministic recurrent communication (ORC) protocol that solves DRCwith bounded delay and no start-up phase.

Synchronization phase.

Coloring phase.

Aplication phase.

Our Solution

The Algorithm

Coloring phase.

Aplication phase.

Our Solution

The Algorithm

Coloring phase.

Aplication phase.

Our Solution

The Algorithm

Coloring phase.

Aplication phase.

Our Solution

The Synchronization Problem

Definition

We say that a protocol solves the synchronization problem if there exists atime t from which the protocol guarantees that the network is synchronized atall times after t, and every node that awakes eventually gets synchronized.The maximum time between a node awaking and getting synchronized is thesynchronization time of the protocol.

Our Solution

Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.

Our Solution

120120

Our Solution

Synchronization Result

Theorem

The synchronization phase solves the synchronization problem under any

∞-adversary with synchronization time T1 + T2, where T1 = 3n2 + 2nT and

T2 = 2nT .

Our Solution

Coloring Phase2r Network

Our Solution

Aplication Phaser Network

Our Solution

Our Results

Theorem

Given a Sensor Network of n nodes, the protocol presented solves the DRC

problem under a τ -adversary with stabilization time at most D · T + τ + n,

where T is the delay of the ORC protocol. The delay of this DRC protocol is

19(k + 1) which is asymptotically optimal, and the message complexity is 0which is optimal.

Theorem

Given a Sensor Network of n nodes, upon being woken up by a ∞-adversary,

the protocol presented solves the DRC problem under an ∞-adversary with

stabilization time at most 6n2 + 4nT + 4n, where T is the delay of the ORC

protocol. The delay of this DRC protocol is 38(k + 1) and the message

complexity is 19(k + 1)/n, which are both asymptotically optimal.

Open Problems

Reduce the stabilization time.

How to merge disconnected components

⇒ extend the failure model.

Open Problems

Reduce the stabilization time.

How to merge disconnected components

⇒ extend the failure model.

Thank you

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