An evaluation of ring-based algorithms for the Eventually Perfect failure detector class

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. Contents • Motivation • Unreliable failure detectors • System model • Communication-efficient implementations of P • A non communication-efficient approach • Performance evaluation • Conclusion

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 • Possibility result (Chandra and Toueg): Consensus can be solved in an asynchronous system subject to failures with an unreliable failure detector

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. 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. Unreliable failure detectors (2)

7. System model • Finite set of n processes  = {p1, p2, ..., pn} 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. Communication-efficient implementations of P • A basic communication-efficient algorithm (LLW0): • each process p sends heartbeats to the processes in the ring between itself (excluded) and its successor succp (included) • p monitors its predecessor predp by hearing heartbeats from it • upon timeout on predp, p suspects it and monitors the predecessor of predp • 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 predp, p builds a new list by merging the list received with its local suspicions. Then, p sets succp to its nearest and non suspected process

9. p1 p2 p3 p4 p6 p5 Communication-efficient implementations of P (2) LLW0 pred1 = p6, succ1 = p2 { p5 } { p5 } pred6 = p5 succ6 = p1 pred6 = p4 succ6 = p1 pred2 = p1 succ2 = p3 { p5 } pred5 = p4 succ5 = p6 pred3 = p2 succ3 = p4 { p5 } pred4 = p3, succ4 = p6 pred4 = p3, succ4 = p5

10. Communication-efficient implementations of P (3) • Providing a faster stabilization of the ring (LLW1): sending sporadic one-to-one messages • upon timeout on predp, p sends (START, p) to pred(predp). Upon reception of this message, pred(predp) sets its successor to p • when p learns that it is erroneously suspecting q, p sends (START, q) to p’s current predp. Upon reception of this message, p’s current predp sets its successor to q • Broadcasting suspicions to reduce the detection latency (LLW2): sending sporadic one-to-all messages • upon timeout on predp, p sends (SUSPICION, predp) to all processes • when a process p is being erroneously suspected, it sends (REFUTATION, p) to all processes

11. p1 p2 p3 p4 p6 p5 (START, p6) Communication-efficient implementations of P (4) LLW1 pred1 = p6, succ1 = p2 { p5 } { p5 } pred6 = p5 succ6 = p1 pred6 = p4 succ6 = p1 pred2 = p1 succ2 = p3 { p5 } pred5 = p4 succ5 = p6 pred3 = p2 succ3 = p4 { p5 } pred4 = p3, succ4 = p6 pred4 = p3, succ4 = p5

12. p1 p2 p3 p4 p6 p5 (SUSPICION, p5) (START, p6) Communication-efficient implementations of P (5) LLW2 pred1 = p6, succ1 = p2 { p5 } { p5 } pred6 = p5 succ6 = p1 pred6 = p4 succ6 = p1 pred2 = p1 succ2 = p3 { p5 } pred5 = p4 succ5 = p6 pred3 = p2 succ3 = p4 { p5 } pred4 = p3, succ4 = p6 pred4 = p3, succ4 = p5

13. A non communication-efficient approach • A basic ring-based algorithm implementing Q: • identical monitoring schema to LLW0 + … • … the list of suspicions does not circulate around the ring • … every process p periodically sends (START, p) to predp. When a process p receives (START, new_succ), it sets succp to new_succ • Providing a faster stabilization of the ring • Transforming Q into P: • propagating suspicions through the ring (LLWQP1) • broadcasting suspicions to reduce the detection latency (LLWQP2)

14. p1 p2 p3 p4 p6 p5 A non communication-efficient approach (2) LLWQ pred1 = p6, succ1 = p2 pred6 = p5 succ6 = p1 pred6 = p4 succ6 = p1 pred2 = p1 succ2 = p3 pred5 = p4 succ5 = p6 pred3 = p2 succ3 = p4 pred4 = p3, succ4 = p5 pred4 = p3, succ4 = p6

15. Performance evaluation

16. Performance evaluation (2)

17. Performance evaluation (3)

18. Performance evaluation (4)

19. Performance evaluation (5)

20. Performance evaluation (6)

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