In an IaaS cloud, virtual machines (VMs), also called instances, may be classified as reserved instances and on-demand instances. The reserved instances having long-term commitments and one-time payment are appropriate for the steady or predictable workloads, while for short-term, spiky or unpredictable workloads, the on-demand instances having flexible hourly payment and no long-term commitments may be more suitable for reducing the cost. In this paper, we consider the economical provisioning of reserved and/or on-demand instances for meeting time-varying computing workload of compute-intensive applications. In order to achieve this, we conceive a strategy for determining the amount of the purchased instances dynamically in order to minimize the total computing cost while keeping quality-of-service (QoS). By mapping QoS as the overload probability, we propose a dynamic instance provisioning strategy based on the large deviation principle, which is capable of calculating the minimum number of instances for the upcoming demands subject to the overload probability below a desired threshold. In addition, a reserved instance provisioning strategy for further reducing the total cost is also proposed by applying the autoregressive (AR) model to calculate the number of reserved instances for the average computation requirements. Finally, the simulations are performed based on real workload traces to show the attainable performance of the proposed instance provisioning strategy for the computing service in an IaaS cloud.