An application provider leases resources (i.e., virtual ma- chine instances) of variable configurations from a IaaS provider over some lease duration (typically one hour). The applica- tion provider (i.e., consumer) would like to minimize their cost while meeting all service level obligations (SLOs). The mechanism of adding and removing resources at runtime is referred to as autoscaling. The process of autoscaling is automated through the use of a management component re- ferred to as an autoscaler. This paper introduces a novel autoscaling approach in which both cloud and application dynamics are modelled in the context of a stochastic, model predictive control problem. The approach exploits trade- off between satisfying performance related objectives for the consumer’s application while minimizing their cost. Simula- tion results are presented demonstrating the efficacy of this new approach.