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
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization2/25
Introduction
Introduction
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization3/25
Introduction
A sensor node
Capabilities
processing
sensing
communication
Limitations
range
memory
life cycle
University of California, Berkeley and
Intel Berkeley Research Lab.
PicoBeacon
Berkeley Wireless Research Center
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization4/25
Introduction
A sensor node
Capabilities
processing
sensing
communication
Limitations
range
memory
life cycle
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization4/25
Introduction
A sensor node
Capabilities
processing
sensing
communication
Limitations
range
memory
life cycle
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization4/25
Introduction
A sensor node
Capabilities
processing
sensing
communication
Limitations
range
memory
life cycle
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization4/25
Introduction
A sensor node
Capabilities
processing
sensing
communication
Limitations
range
memory
life cycle
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization4/25
Introduction
A sensor node
Capabilities
processing
sensing
communication
Limitations
range
memory
life cycle
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization4/25
Model and Problem Definition
Model and Problem Definition
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization5/25
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization6/25
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization6/25
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization6/25
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization6/25
Model and Problem Definition
Network model: Geometric Graph
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization7/25
Model and Problem Definition
Network model: Geometric Graph
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization7/25
Model and Problem Definition
Network model: Geometric Graph
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization7/25
Model and Problem Definition
Network model: Geometric Graph
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization7/25
Model and Problem Definition
Network model: Geometric Graph
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization7/25
Model and Problem Definition
Network model: Geometric Graph
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization7/25
Model and Problem Definition
Network model: Geometric Graph
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization7/25
Model and Problem Definition
Network model: Geometric Graph
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization7/25
Model and Problem Definition
Network model: Geometric Graph
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization7/25
Model and Problem Definition
Network model: Geometric Graph
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization7/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization8/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization8/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization8/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization8/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization9/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization9/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization9/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization10/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization11/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization12/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization12/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization12/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization12/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization13/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization13/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization13/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization13/25
Model and Problem Definition
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization14/25
Our Solution
Our Solution
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization15/25
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization16/25
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization16/25
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization16/25
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization16/25
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization17/25
Our Solution
Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.
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A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization18/25
Our Solution
Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.
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A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization18/25
Our Solution
Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.
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A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization18/25
Our Solution
Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.
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A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization18/25
Our Solution
Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.
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A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization18/25
Our Solution
Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.
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A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization18/25
Our Solution
Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.
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A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization18/25
Our Solution
Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.
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A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization18/25
Our Solution
Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.
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A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization18/25
Our Solution
Synchronization Phase (r Network)M. G. Gouda and T. Herman, Stabilizing Unison. IPL, 1990.
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A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization18/25
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 .
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization19/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Coloring Phase2r Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization20/25
Our Solution
Aplication Phaser Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization21/25
Our Solution
Aplication Phaser Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization21/25
Our Solution
Aplication Phaser Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization21/25
Our Solution
Aplication Phaser Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization21/25
Our Solution
Aplication Phaser Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization21/25
Our Solution
Aplication Phaser Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization21/25
Our Solution
Aplication Phaser Network
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization21/25
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.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization22/25
Open Problems
Open Problems
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization23/25
Open Problems
Open Problems
Reduce the stabilization time.
How to merge disconnected components
⇒ extend the failure model.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization24/25
Open Problems
Open Problems
Reduce the stabilization time.
How to merge disconnected components
⇒ extend the failure model.
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization24/25
Thank you
A. Fernandez Anta, M. A. Mosteiro, Christopher Thraves Deterministic Recurrent Communication and Synchronization25/25