1 eventual leader election in evolving mobile networks luciana arantes 1, fabiola greve 2,...

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Eventual Leader Electionin Evolving Mobile Networks

Luciana Arantes1, Fabiola Greve2, Véronique Simon1, and Pierre Sens1

1Université de Paris 6 (LIP6) / CNRS/ INRIA, France 2 DCC – Federal University of Bahia, Brazil

OPODIS, Nice, Dec. 2013

OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA

Roadmap

Context/Motivation

Model for dynamic network

Eventual election algorithm

Conclusion

OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 2


Dynamic self-organized systems Wireless ad-hoc networks (WMN, WSN)

Key features Unknown membership Multi-hop networks Dynamic changing topology

churn, node mobility Transmission range communication

broadcast to neighborhood Asynchronous systems

no bound on processor speed and transmission delays

Context

Eventual election

The Ω failure detector satisfies (“eventual leader election”):

there is a time after which every correct process always trusts the same correct process

Ω is the weakest failure detector for solving Consensus in the crash failure model


Context

p1

p3

p4 p5

p2

Ω=p2

Ω=p2

Ω=p2

correct

crashed

Model for Failure Detection in Dynamic Networks

The membership is unknown A node is not aware about the set of nodes nor the number of them.

Finite arrival model The network is dynamic composed of infinite mobile nodes, but each run consist

of a finite set n nodes. The system is asynchronous

There are no assumptions on the relative speed of processes nor on message transfer delays.

Communication Channels are fair-lossy there is no message duplication, modification or creation


Note: node = process

Model (cont’d)

Communication graph is dynamic Dynamic topology represented by a time-varying graph

(TVG) [CFQS11] : TVG = <Nodes, Edges, Time, EdgePresence, Latency, NodePresence>

A node p can reach q if there exists a journey between p and q (i.e., a path over time between p and q)

p q

time 1 2 3

p r r s s qLatency 0.5 0.7 1


Processes status

Let knownq set denotes the partial knowledge of q.

2 sets of nodes :

STABLE (correct): nodes eventually and permanently correct

FAULTY: nodes which crash


Transmission range

mobile node

Stable node

Model

Network connectivity

Transmission TVG induced by the stable communicating nodes in the system A message sent at time t induces an edge at t in the

transmission TVG

Network recurrent connectivity TVG of class 5

There exists a journey between all stable nodes at any time Eventually, the transmission TVG is connected other time


Timer-based x Timer-free assumptions

The Ω failure can not be implemented in a pure asynchronous system Two approaches:

Timer-based Constraint to satisfy message transfer delays Channels are eventually timely

Message exchange pattern Constraint to satisfy a message delivery order Query-response mechanism


Properties to implement an

Stable Termination Property (SatP): Each QUERY must be received by at least one stable and

known node Necessary for the diffusion of the information

Stabilized Responsiveness Property (SRP): There exists a time t after which all nodes of pi 's

neighborhood receive, to every of their queries, a response from pi which is always among the first responses

SRP should be hold for at least one stable known node (the eventual leader)


An Eventual Leader Election Algorithm

Principle Election of a leader process based on punishment Periodic local query-response exchange

Wait for responses If pj, locally known by pi, does not respond to a query of p

among i, pj is punished by pi.

Exchange of information


r not punished

r punished

r not punished

p

qWaiting for q responses

…

r

Ne

igh

bo

rho

od

q

An Eventual Leader Election Algorithm

Notation (pi) midi: a counter to timestamp every query-response message;

local_knowni: the current knowledge of pi about its neighborhood set of tuples <midj,pj>; max known midj

global_knowni: the current knowledge of pi about the membership of the system set of tuples <midj,pj>; max known midj

punishi: punished processes by pi

set of tuples <ct,p>

Query and Response message from pi

<midi, punishi, global_knowni>


Leader Election: Sending of Query


punishment

* - pj is a neighbor of pi, - pj does not answer to pi, - pj is not suspected to have moved

*

Reception of Query and Response;Invocation of the Leader


*

*

*update of pi’s state about punishment, membership, and pi’s neighborhood with more recent information : keeps the tuples with the greatest counter.

*process with the smallest counter

*

15

Exemple: Mobility of nodes

1

2

3

<1,1>,<1,2>,<1,3>,<1,4>

<0,1>

<1,2>,<1,3>,<1,4>

4

local_known1

punished1

global_known1

<2,4>

<0,1>,<1,4> <0,1>,<2,4>

x:<x,4> in local_known1 < y:<y,4> in global_known1

OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA

<0,1>,<3,4>

1 stops punishing 4

5

<1,2>,<1,3>,<2,4>

Conclusion

Model and and a timer-free algorithm to solve the eventual leader election in mobile dynamic systems

The algorithm implement the Ω class of failure detectors using: Query-response approach

Failure detection and exchange of information TGV framework

Dynamics of the Network


Thank you


1 eventual leader election in evolving mobile networks luciana arantes 1, fabiola greve 2,...

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