Distributed Algorithms for Failure Detection in Crash Environments R. Cortiñas, A. Lafuente, M. Larrea Distributed Systems Group University of the Basque Country UPV/EHU

Guest Stars: P, S and Omega P: strong completeness, eventual strong accuracy Eventually every process that crashes is permanently suspected by every correct process There is a time after which correct processes are not suspected by any correct process S: strong completeness, eventual weak accuracy There is a time after which some correct process is never suspected by any correct process Omega: eventual leader election There is a time after which all the correct processes always trust the same correct process Master SIA – Sistemas Distribuidos

The First P Algorithm [CT96] Master SIA – Sistemas Distribuidos

Communication Optimality A ring arrangement of processes Master SIA – Sistemas Distribuidos

Communication Optimality Communication-efficient algorithms: n links are used forever Master SIA – Sistemas Distribuidos

Communication Optimality Communication-optimal algorithms: C links are used forever Master SIA – Sistemas Distribuidos

Communication-optimal P Master SIA – Sistemas Distribuidos

Communication-optimal Omega We also propose an optimal implementation of S, the weakest failure detector for solving Consensus: processes ordered: p1, ..., pn heartbeat strategy communication pattern: one-to-successors based on a trusted process (instead of a list of suspected processes) Master SIA – Sistemas Distribuidos

Communication-optimal Omega i) Initially, p1 starts sending messages periodically to the rest of processes, and all processes trust p1 p1 p2 p3 p4 p5 trusted1 = p1 trusted2 = p1 trusted3 = p1 trusted4 = p1 trusted5 = p1 Master SIA – Sistemas Distribuidos

Communication-optimal Omega ii) If a process does not receive a message within some timeout period from its trusted process pi, then it suspects pi and takes the next process pi+1 as its new trusted process p1 p2 p3 p4 p5 trusted1 = p1 trusted2 = p1 trusted3 = p1 timeout on p1 trusted4 = p2 trusted5 = p1 Master SIA – Sistemas Distribuidos

Communication-optimal Omega iii) If a process trusts itself, then it starts sending messages periodically to its successors p1 p2 p3 p4 p5 trusted1 = p1 timeout on p1 trusted2 = p2 trusted3 = p1 trusted4 = p2 trusted5 = p1 Master SIA – Sistemas Distribuidos

Communication-optimal Omega iv) If a process receives a message from a process pi preceding its trusted process, then it will trust pi again, increasing its timeout period with respect to pi p1 p2 p3 p4 p5 trusted1 = p1 message from p1 trusted2 = p1 timeout_period21++ trusted3 = p2 message from p1 trusted4 = p1 timeout_period41++ trusted5 = p1 Master SIA – Sistemas Distribuidos

Communication-optimal Omega Lemma. With the previous algorithm, eventually all the correct processes will permanently trust the first correct process in p1, ..., pn This property trivially allows us to provide the properties of S: Eventual weak accuracy: by not suspecting the trusted process Strong completeness: by suspecting all the processes except the trusted process Master SIA – Sistemas Distribuidos

Communication-optimal Omega Master SIA – Sistemas Distribuidos