The effect of forgetting on the performance of a synchronizer

Abstract We study variants of the α -synchronizer by Awerbuch (1985) within a distributed message passing system with probabilistic message loss. The purpose of a synchronizer is to maintain a virtual (lock-step) round structure, which simplifies the design of higher-level distributed algorithms. The underlying idea of an α -synchronizer 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 the current round. In this work, we study the performance of several synchronizers in an environment with probabilistic message loss. In particular, we analyze how different strategies of forgetting affect the round durations. The synchronizer variants considered differ in the times when processes discard part of their accumulated knowledge during the execution. Possible applications can be found, e.g., in sensor fusion, where sensor data become outdated and thus invalid after a certain amount of time. For all synchronizer variants considered, we develop corresponding Markov chain models and quantify the performance degradation using both analytic approaches and Monte-Carlo simulations. Our results allow to explicitly calculate the asymptotic behavior of the round durations: While in systems with very reliable communication the effect of forgetting is negligible, the effect is more profound in systems with less reliable communication. Our study thus provides computationally efficient bounds on the performance of the (non-forgetting) α -synchronizer and allows to quantitatively assess the effect accumulated knowledge has on the performance.