On sample-path staleness in lazy data replication

We analyze synchronization issues arising between two stochastic point processes, one of which models data churn at an information source and the other periodic downloads from its replica (e.g., search engine, web cache, distributed database). Due to lazy (pull-based) synchronization, the replica experiences recurrent staleness, which translates into some form of penalty stemming from its reduced ability to perform consistent computation and/or provide up-to-date responses to customer requests. We model this system under non-Poisson update/refresh processes and obtain sample-path averages of various metrics of staleness cost, generalizing previous results and exposing novel problems in this field.