Probabilistic quorum systems for dependable distributed data management

Among failure-prone and dynamic distributed systems there is a significant class of systems that strive for high availability and can function with inconsistent data. Examples include flight reservation systems which allow overbooking or emergency ambulance systems which return informative responses to time-critical queries. Data replication is a well-known technique for tolerating failures and dependably managing data in distributed systems. For this purpose quorums are used for executing the basic operations: writing new data and reading previously written data. Strict quorum systems rely on a strict consistency notion called sequential consistency by ensuring the mutual exclusion between read and write operations as well as write and write operations. The guarantee of this strict consistency limits their availability. Probabilistic quorum systems increase the availability of operations by relaxing the previously mentioned mutual exclusions. This relaxation requires the mutual exclusion and therefore the intersections of quorums to hold only with high probability for read and write as well as write and write probabilistic operations. The first contribution of this work is the construction of probabilistic quorum systems based on strict quorum systems as input. The generation, selection, and integration of quorums are identified as steps of the construction. The selection is driven by consistency by putting emphasis on the intersections with the previous operation’s quorums. Additionally, they preserve beneficent characteristics of the original underlying strict quorum systems (e.g., operation availability, communication costs, etc.). Furthermore in the integration step, different priorities are considered when combining strict and probabilistic quorums to obtain different resulting probabilistic quorum systems. These combination methods are called integration strategies. The second contribution of this thesis is the analysis of different probabilistic quorum system constructions with respect to the trade-off between data consistency and operation availabilities. By means of a Markov chain analysis, qualitative and quantitative aspects of the trade-off are identified. The empirical results strongly indicate that there is a total order among the three introduced integration strategies with respect to data consistency independent of the particular investigated replication strategy. The third contribution is the optimization of probabilistic quorum systems in terms of data consistency and operation availabilities. Concepts and methods from the area of strict quorum systems are extended for the area of probabilistic quorum systems. In this context, it is proven that only a single non-dominated probabilistic quorum system exists and that only the write-write intersection of so-called availability-symmetric probabilistic quorum systems can be relaxed. Additionally, a graphical data consistency measure is presented. Although this measure is more abstract than the one used in the Markov chain analysis, it allows to identify availability-symmetric quorum systems that exhibit maximal data consistency with respect to another quorum system and with respect to a particular, fixed operation. The closing contribution of the work is the general analysis of data consistency with respect to the integrations of probabilistic quorum systems for an arbitrary number of processes in a distributed system. This analysis formally proves and generalizes the results from the previous Markov chain analysis.