With the advent of big data era, the data analytical applications have sprung up which can be modeled using workflow. Such workflow applications are subject to continuously arriving requests and have a rigid requirement on response time. When running the analytical workflow in a cloud platform, one of the critical questions arising here is that how to provision resources in a way that the monetary cost can be reduced under the constraint of the response time. In this paper, we use queueing network theory to address this challenge. First, we present the performance analytic model for the elastic analytical workflows based on queueing network theory. Then, we design a resource provision strategy to determine the number of virtual machines for individual component of the applications with response time constraint. Simulation experiments using the real workload trace data show that our proposed approach provides a simple yet powerful solution to provision resources for analytical workflows under dynamic workload conditions.