This article considers NoSQL database replication problems. It analyzes the influence of the N, W, R replication parameters on the consistency characteristics of database record replicas (N -- the total number of one record's replicas, W -- number of replicas for write operation execution into a database, R -- number of replicas for record read operation execution from a database). It describes a developed model for eventual consistency (W+R=N), obtaining probability estimate that during the process of N-W replica updates there will be at least one read request out of non-updated replicas. It also proposes a model for strong consistency of the replicas in NoSQL databases, which allows for estimation of random wait time of the read request for the record update completion. It describes the process for preparation and execution of experiments in the cloud for model calibration and its validation.