The effect of forgetting on the performance of a synchronizer

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.