1. 1 Eventual Leader Election in Evolving Mobile Networks Luciana Arantes 1, Fabiola Greve 2, Véronique Simon 1, and Pierre Sens 1 1 Université 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

2. Roadmap Context/Motivation Model for dynamic network Eventual election algorithm Conclusion OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 2

3. 3 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

4. 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 OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 4 Context p1 p3 p4 p5 p2 Ω=p 2 correct crashed

5. 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 OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 5 Note: node = process

6. Model (cont’d) Communication graph is dynamic  Dynamic topology represented by a time-varying graph (TVG) [CFQS11] : TVG =  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 q Latency 0.5 0.7 1 OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 6

7. Processes status Let known q set denotes the partial knowledge of q. 2 sets of nodes :  STABLE (correct): nodes eventually and permanently correct  FAULTY: nodes which crash OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 7 Transmission range mobile node Stable node Model

8. 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 OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 8

9. 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 OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 9

10. 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 p i 's neighborhood receive, to every of their queries, a response from p i which is always among the first responses SRP should be hold for at least one stable known node (the eventual leader) OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 10

11. An Eventual Leader Election Algorithm Principle  Election of a leader process based on punishment  Periodic local query-response exchange Wait for  responses  If p j, locally known by p i, does not respond to a query of p among  i, p j is punished by p i. Exchange of information OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 11 r not punished r punished r not punished p q Waiting for  q responses … r Neighborho od qq

12. An Eventual Leader Election Algorithm Notation (p i )  mid i : a counter to timestamp every query-response message;  local_known i : the current knowledge of p i about its neighborhood set of tuples ; max known mid j  global_known i : the current knowledge of p i about the membership of the system set of tuples ; max known mid j  punish i : punished processes by p i set of tuples Query and Response message from p i  OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 12

13. Leader Election: Sending of Query OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 13 punishment * - p j is a neighbor of p i, - p j does not answer to p i, - p j is not suspected to have moved *

14. Reception of Query and Response; Invocation of the Leader OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 14 * * *update of p i ’s state about punishment, membership, and p i ’s neighborhood with more recent information : keeps the tuples with the greatest counter. *process with the smallest counter *

15. 15 Exemple: Mobility of nodes 1 2 3,,,,, 4 local_known 1 punished 1 global_known 1, x: in local_known 1 in global_known 1 OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA, 1 stops punishing 4 5,,

16. 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 OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 16

17. Thank you OPODIS 2013: Paris 6 (CNRS/INRIA) and UFBA 17