UPV - EHU An Evaluation of Communication-Optimal P Algorithms Mikel Larrea Iratxe Soraluze Roberto Cortiñas Alberto Lafuente Department of Computer Architecture and Technology The University of the Basque Country

UPV - EHU 2 PDP 2008 − Toulouse, France, February 13-15, 2008 Contents Motivation System Model Communication Optimality The Algorithms Complexity Analysis Performance Evaluation Conclusion

UPV - EHU 3 PDP 2008 − Toulouse, France, February 13-15, 2008 Motivation Unreliable failure detectors have been used to address Consensus and related problems in asynchronous crash-prone distributed systems –Theory: impossibility/possibility results, minimality results –Practice: efficient implementations and transformations The P class satisfies the following properties –Strong Completeness: eventually every process that crashes is permanently suspected by every correct process –Eventual Strong Accuracy: there is a time after which correct processes are not suspected by any correct process

UPV - EHU 4 PDP 2008 − Toulouse, France, February 13-15, 2008 Communication efficiency –Number of links used forever –Periodic communication cost Non communication-efficient algorithms Communication-efficient algorithms Communication-optimal algorithms Motivation: Implementing P Efficiently ring-based } Sporadic communication overhead –Number of messages to manage a suspicion Quality of Service –Query accuracy probability –Crash detection latency

UPV - EHU 5 PDP 2008 − Toulouse, France, February 13-15, 2008 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, one in each direction Processes can fail by crashing. Once a process crashes, it does not recover –Up to n-1 processes may crash –C is the (unknown) number of correct processes Processes are arranged in a logical ring Partially synchronous system

UPV - EHU 6 PDP 2008 − Toulouse, France, February 13-15, 2008 p1p1 p3p3 p4p4 p6p6 p5p5 p2p2 Communication Optimality A ring arrangement of processes

UPV - EHU 7 PDP 2008 − Toulouse, France, February 13-15, 2008 p1p1 p3p3 p4p4 p6p6 p5p5 p2p2 Communication Optimality Communication-efficient algorithms: n links are used forever

UPV - EHU 8 PDP 2008 − Toulouse, France, February 13-15, 2008 p1p1 p3p3 p4p4 p6p6 p5p5 p2p2 Communication Optimality Communication-optimal algorithms: C links are used forever

UPV - EHU 9 PDP 2008 − Toulouse, France, February 13-15, 2008 The Algorithms We have implemented several ring-based communication-optimal P algorithms Algorithms are based on reporting failure suspicions (and suspicion refutations) Three communication patterns –Algorithm 1: based on Reliable Broadcast RBcast is a communication primitive guaranteeing that all correct processes deliver the same set of messages. This set includes at least all messages broadcast by correct processes –Algorithm 2: based on one-to-one communication –Algorithm 3: based on one-to-all communication

UPV - EHU 10 PDP 2008 − Toulouse, France, February 13-15, 2008 The Algorithms Algorithm 1: RBcast-based p1p1 p3p3 p4p4 p6p6 p5p5 p2p2 O(n 2 ) messages required to communicate a suspicion Low crash detection latency

UPV - EHU 11 PDP 2008 − Toulouse, France, February 13-15, 2008 The Algorithms Algorithm 2: one-to-one based p1p1 p3p3 p4p4 p6p6 p5p5 p2p2 Suspected 1 = {p 3, p 5, p 6 } O(n) messages required to communicate a suspicion High crash detection latency

UPV - EHU 12 PDP 2008 − Toulouse, France, February 13-15, 2008 The Algorithms Algorithm 3: one-to-all based p1p1 p3p3 p4p4 p6p6 p5p5 p2p2 Suspected 1 = {p 3, p 5, p 6 } O(n) messages required to communicate a suspicion Low crash detection latency

UPV - EHU 13 PDP 2008 − Toulouse, France, February 13-15, 2008 Complexity Analysis

UPV - EHU 14 PDP 2008 − Toulouse, France, February 13-15, 2008 Performance Evaluation: Query Accuracy

UPV - EHU 15 PDP 2008 − Toulouse, France, February 13-15, 2008 Performance Evaluation: Crash Detection Latency

UPV - EHU 16 PDP 2008 − Toulouse, France, February 13-15, 2008 Conclusion We have presented several communication- optimal algorithms implementing P Which to use: Algorithm 2 or Algorithm 3? Best choice: hybrid approach –Initially (erroneous suspicions), use Algorithm 2 –When the ring has probably stabilized, switch to Algorithm 3 –Issues What about crashes during stabilization? How do we know (guess) that the system has stabilized?

UPV - EHU 17 PDP 2008 − Toulouse, France, February 13-15, 2008 ? Questions

UPV - EHU 18 PDP 2008 − Toulouse, France, February 13-15, 2008 Future Work Current scenario: –Local area network settings –Uniform communication delays –1-to-all communication supported easily (Ethernet, WiFi) Future scenario: –Wide area network settings –Non-uniform communication delays –1-to-all communication not supported –Local communication patterns required For periodic messages (heartbeats)  ring For sporadic messages (suspicions and refutations)