1. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class Joachim Wieland Mikel Larrea Alberto Lafuente The University of the Basque Country

2. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 2 Contents Motivation Unreliable failure detectors System model Communication-efficient implementations of  P A non communication-efficient approach Performance evaluation Conclusion

3. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 3 Motivation FLP impossibility result (Fischer, Lynch, and Paterson): Consensus cannot be solved deterministically in an asynchronous system subject to even a single process crash nre Possibility result (Chandra and Toueg): Consensus can be solved in an asynchronous system subject to failures with an unreliable failure detector

4. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 4 Motivation (2) Evaluate different ring-based algorithms for  P Two kinds of performance parameters: – Communication efficiency – Quality of service Two families of algorithms: – Communication-efficient  P + some optimizations – Non communication-efficient  Q + transformation to  P modular approach designed with quality of service in mind

5. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 5 Unreliable failure detectors Distributed oracle that provides (possibly incorrect) hints about the operational status of other processes Abstractly characterized in terms of two properties: completeness and accuracy – Completeness characterizes the degree to which crashed processes are suspected by correct processes – Accuracy characterizes the degree to which correct processes are not suspected, i.e., restricts the false suspicions that a failure detector can make

6. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 6 Unreliable failure detectors (2)

7. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 7 System model Finite set of n processes  = {p 1, p 2,..., p n } that communicate only by message-passing Every pair of processes is connected by two unidirectional and reliable communication links Processes can fail by crashing. Once a process crashes, it does not recover Processes are arranged in a logical ring Partially synchronous system

8. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 8 Communication-efficient implementations of  P A basic communication-efficient algorithm (LLW 0 ): – each process p sends heartbeats to the processes in the ring between itself (excluded) and its successor succ p (included) – p monitors its predecessor pred p by hearing heartbeats from it upon timeout on pred p, p suspects it and monitors the predecessor of pred p – if p erroneously suspected q, p starts monitoring q again – processes propagate the list of suspicions around the ring, piggybacked in the heartbeats upon reception of the list of suspicions from pred p, p builds a new list by merging the list received with its local suspicions. Then, p sets succ p to its nearest and non suspected process

9. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 9 Communication-efficient implementations of  P (2) p1p1 p2p2 p3p3 p4p4 p6p6 p5p5 pred 1 = p 6, succ 1 = p 2 pred 2 = p 1 succ 2 = p 3 pred 3 = p 2 succ 3 = p 4 pred 4 = p 3, succ 4 = p 5 pred 5 = p 4 succ 5 = p 6 pred 6 = p 5 succ 6 = p 1 pred 6 = p 4 succ 6 = p 1 { p 5 } pred 4 = p 3, succ 4 = p 6 LLW 0

10. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 10 Communication-efficient implementations of  P (3) Providing a faster stabilization of the ring (LLW 1 ): sending sporadic one-to-one messages – upon timeout on pred p, p sends (START, p) to pred(pred p ). Upon reception of this message, pred(pred p ) sets its successor to p – when p learns that it is erroneously suspecting q, p sends (START, q) to p’s current pred p. Upon reception of this message, p’s current pred p sets its successor to q Broadcasting suspicions to reduce the detection latency (LLW 2 ): sending sporadic one-to-all messages – upon timeout on pred p, p sends (SUSPICION, pred p ) to all processes – when a process p is being erroneously suspected, it sends (REFUTATION, p) to all processes

11. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 11 Communication-efficient implementations of  P (4) p1p1 p2p2 p3p3 p4p4 p6p6 p5p5 pred 1 = p 6, succ 1 = p 2 pred 2 = p 1 succ 2 = p 3 pred 3 = p 2 succ 3 = p 4 pred 4 = p 3, succ 4 = p 5 pred 5 = p 4 succ 5 = p 6 pred 6 = p 5 succ 6 = p 1 pred 6 = p 4 succ 6 = p 1 { p 5 } pred 4 = p 3, succ 4 = p 6 (START, p 6 ) LLW 1

12. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 12 Communication-efficient implementations of  P (5) p1p1 p2p2 p3p3 p4p4 p6p6 p5p5 pred 1 = p 6, succ 1 = p 2 pred 2 = p 1 succ 2 = p 3 pred 3 = p 2 succ 3 = p 4 pred 4 = p 3, succ 4 = p 5 pred 5 = p 4 succ 5 = p 6 pred 6 = p 5 succ 6 = p 1 pred 6 = p 4 succ 6 = p 1 { p 5 } pred 4 = p 3, succ 4 = p 6 (SUSPICION, p 5 ) (START, p 6 ) LLW 2

13. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 13 A non communication-efficient approach A basic ring-based algorithm implementing  Q: – identical monitoring schema to LLW 0 + … – … the list of suspicions does not circulate around the ring – … every process p periodically sends (START, p) to pred p. When a process p receives (START, new_succ), it sets succ p to new_succ Providing a faster stabilization of the ring Transforming  Q into  P: – propagating suspicions through the ring (LLW QP1 ) – broadcasting suspicions to reduce the detection latency (LLW QP2 )

14. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 14 A non communication-efficient approach (2) p1p1 p2p2 p3p3 p4p4 p6p6 p5p5 pred 1 = p 6, succ 1 = p 2 pred 2 = p 1 succ 2 = p 3 pred 3 = p 2 succ 3 = p 4 pred 4 = p 3, succ 4 = p 5 pred 5 = p 4 succ 5 = p 6 pred 6 = p 5 succ 6 = p 1 pred 6 = p 4 succ 6 = p 1 pred 4 = p 3, succ 4 = p 6 LLW Q

15. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 15 Performance evaluation

16. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 16 Performance evaluation (2)

17. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 17 Performance evaluation (3)

18. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 18 Performance evaluation (4)

19. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 19 Performance evaluation (5)

20. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 20 Performance evaluation (6)

21. An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 21 Conclusion Evaluation of two families of heartbeat-, ring-based algorithms implementing  P Communication-efficient family – n links are eventually used Non communication-efficient family – modular approach – n + C links are eventually used (with 1 ≤ C ≤ n) – better quality of service