We study variants of the \(\alpha \)-synchronizer by Awerbuch (J. ACM, 1985) within a distributed message passing system with probabilistic message loss. The purpose of synchronizers is to maintain a virtual (discrete) round structure. Their idea essentially is to let processes continuously exchange round numbers and to allow a process to proceed to the next round only after it has witnessed that all processes have already started its own current round.
In this work, we study how four different, naturally chosen, strategies of forgetting affect the performance of these synchronizers. The variants differ in the times when processes discard part of their accumulated knowledge during execution. Such actively forgetting synchronizers have applications, e.g., in sensor fusion where sensor data becomes outdated and thus invalid after a certain amount of time.
We give analytical formulas to quantify the degradation of the synchronizers’ performance in an environment with probabilistic message loss. In particular, the formulas allow to explicitly calculate the performance’s asymptotic behavior. Interestingly, all considered synchronizer variants behave similarly in systems with low message loss, while one variant shows fundamentally different behavior from the remaining three in systems with high message loss. The theoretical results are backed up by Monte-Carlo simulations.
Markov Chain Model Steady State Distribution Round Number Current Round Message Loss
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