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This paper presents a Markovian analytical model to estimate service response time for elastic cloud applications. Given the expected application workload, the number of virtual machine (VM) instances, and the capacity of each VM instance, the model can approximate the mean service time. The mean service time is a critical metric to estimate, and contributes to the SLA end-to-end response time experienced by application users. The end-to-end response time is an aggregated delay of the service time in addition to delays incurred at the network nodes and links. Our analytical model focuses on estimating the mean service time; however, the model is sufficiently general and can be extremely useful in studying cloud performance. Equations for key performance measures are derived. These measures include mean response time, throughput, request loss, queueing probability, and CPU utilization. The correctness of the model has been verified using discrete-event simulation.