Cloud computing has risen as a new computing paradigm providing computing, resources for networking, and storage as a service across the network. Data replication is a phenomenon which brings the available and reliable data (e.g., maybe the databases) nearer to the consumers (e.g., cloud applications) to overcome the bottleneck and is becoming a suitable solution. In this paper, the authors study the performance characteristics of a replicated database in cloud computing data centres which improves QoS by reducing communication delays. They formulate a theoretical queueing model of the replicated system by considering the arrival process as Poisson distribution for both types of client request, such as read and write applications. They solve the proposed model with the help of the recursive method, and the relevant performance matrices are derived. The evaluated results from both the mathematical model and extensive simulations help to study the unveil performance and guide the cloud providers for modelling future data replication solutions.