Beyond Lamport, Towards Probabilistic Fair Ordering

A growing class of applications demands \emph{fair ordering} of events, which ensures that events generated earlier are processed before later events. However, achieving such sequencing is challenging due to the inherent errors in clock synchronization: two events at two clients generated close together may have timestamps that cannot be compared confidently. We advocate for an approach that embraces, rather than eliminates, clock synchronization errors. Instead of attempting to remove the error from a timestamp, \systemname{}, our proposed system, leverages a statistical model to compare two noisy timestamps probabilistically by learning per-clock synchronization error distributions. Our preliminary statistical model computes the probability that one event precedes another by only relying on local clocks of clients. This serves as a foundation for a new relation: \emph{likely-happened-before} denoted by $\xrightarrow{p}$ where $p$ represents the probability that an event happened before another. The $\xrightarrow{p}$ relation provides a basis for ordering multiple events which are otherwise considered \emph{concurrent} by Lamport's \emph{happened-before} ($\rightarrow$) relation. We highlight various related challenges including the intransitivity of the $\xrightarrow{p}$ relation as opposed to the transitive $\rightarrow$ relation. We outline several research directions: online fair sequencing, stochastically fair total ordering, and handling byzantine clients.