Dynamic regular registers in systems with churn

Distributed systems with churn, or dynamic distributed systems, allow the processes to join and leave the system at will. In this paper, we present a new consistency condition for shared read-write registers which is based on multi-writer regularity, but allows for the likelihood of the register to lose its state with some probability; we call this a dynamic regular register. We then describe an algorithm for implementing a dynamic regular register using copies of the register distributed among the processes. When a process joins the system, it attempts to obtain an up-to-date copy of the data from other processes. Copies of the register are updated by broadcasting information. To model the dynamicity of the register system with churn, we use a continuous-time birth-death process which is a special case of continuous-time Markov processes. Then, we analyze the probability and the time duration that the dynamic regular register system keeps its state, given the joining rate and the leaving rate of the processes.