Purpose of research. The object of the study is a network cloud service built on the basis of a replicated database. Data in distributed computing systems are replicated in order to ensure the reliability of their storage, facilitate access to data as well as to improve the storage system performance. In this regard, the problem of analyzing the effectiveness of processing the queries to replicated databases in a network-based cloud environment, and, in particular, the problem of organizing priority query queues for updating databae copies (update requests) and for searching and reading information in databases (query-requests). The purpose of this work is to study and organize priority modes in a network distributed computing system with cloud service architecture.Methods. The study was conducted on the basis of two types of behavioural patterns: models based on Petri nets to describe and verify the functioning of a distributed computing system with replicated databases represented as a pool of resource units with several units, and models based on the GPSS simulation language for possible evaluation of passage of query time of each type in queues depending on the priority of queries.Results. Based on two simulation methods, the operation of a cloud system with database replicas was analyzed. In this system two distributed cloud computing systems interact: MANET Cloud based on a wireless network and Internet Cloud based on the Internet. These databases together are the basis of the DBaaSoD (Data Bases as a Service on Demand) cloud service (databases as a service organized at user’s query). To study this system the models of two classes were developed. The model based on Petri nets is designed to test the simulated distributed application for proper functioning. The decisions on the mapping of Petri nets on the architecture of computer networks are discussed. The simulation statistical model is used to compare the priority and non-priority maintenance modes of query- and update-requests by the criterion of average passage of time of queries in queues.Conclusion. System models based on Petri nets were tested, which showed their liveness and security, which makes it possible to move from models to building formalized specifications for network applications for network cloud services in distributed computing systems with replicated databases. The study of GPSS-model showed that in the case of priority service of update-requests, the time of passage for them is reduced by about 2 to 4 times compared with query-requests, depending on the intensity of the query-requests. In the non-priority mode, the serving conditions for update-queries deteriorate and the time of passage in the queue for them increases by about 2 to 6 times as compared with query-requests depending on the intensity of the query-requests.