Joint pricing and capacity planning for IaaS cloud

We consider a monopoly Infrastructure-as-a-Service (IaaS) provider market with a set of Software-as-a-Service (SaaS) providers, where each SaaS provider lease the virtual machines (VMs) from the IaaS provider to provide cloud-based application services to its end-users. We investigate the problem of designing a joint pricing and capacity planning scheme from the IaaS provider's perspective. Specifically, we first study the SaaS providers' optimal decisions in terms of the amount of end-user requests to admit and the number of VMs to lease, given the resource price charged by the IaaS provider. Next, based on the best responses of the SaaS providers, we study joint pricing and capacity planning to maximize the IaaS provider's profit, which is determined by the revenue obtained through supplying the VMs and the energy cost for maintaining the active servers. By exploring the relationship between the optimal capacity and price, we simplify the original optimization problem into the a convex problem with respect to the price, and then we derive the expressions of the optimal solutions. Finally, the numerical results illustrate the efficacy of our proposed joint pricing and capacity planning scheme.