IHFD: an improved heartbeat-based failure detector of $$\Diamond \,P$$ class for partially synchronous hierarchical distributed systems

Abstract

Fundamentally, failure detectors are important for failure detection in distributed systems, particularly in partially synchronous environments, where message delays and process failures are unavoidable. This paper proposed an Improved Heartbeat-based Failure Detector (IHFD) for hierarchical distributed systems that combines adaptive timeout-based estimation, statistical deviation handling, and structured failure results aggregation within a health monitoring tree (HMT). By integrating local failure detection and classification into a global health monitoring tree (GlobalHMT), the proposed algorithm provides a consolidated, system-wide view of node health at the root level. The performance evaluation of IHFD is conducted using real-world PlanetLab heartbeat traces and compared against six state-of-the-art failure detectors, including HFD, Chen, Bertier, PHI, EDFD, and 2WFD failure detectors. At the root monitoring node, IHFD achieves a Mistake Rate of \(6.6 \times 10^{-5}\) , and a Query Accuracy Probability of 0.9999. Across all hierarchy levels, IHFD maintains Mistake Rate values of (0.066– \(2.731)\times 10^{-3}\) , while Bertier and PHI record substantially higher ranges of (34.391– \(53.061)\times 10^{-3}\) and (40.170– \(58.258)\times 10^{-3}\) , respectively. The Relative Root Mean Square Error (RRMSE) values of 2.133–4.411 further indicate bounded detection time variability, and the FGPD reaches \(18.5\times 10^{6}\,{\text {ms}}\) at the Parent 3 monitoring node, demonstrating sustained failure-free operation between false suspicion events. The Forward Good Period Duration reaches \(18.5 \times 10^6\,{\text {ms}}\) at Parent 3 monitoring node, demonstrating sustained failure-free operations between failure detection events. In addition, IHFD guarantees eventually strong accuracy and strong completeness, which places it within the Eventually Perfect \(\Diamond \,P\) class of failure detectors.