Optimal pricing and service provisioning strategies in cloud systems: a Stackelberg game approach

Cloud computing is a recent advancement where service providers offer hardware infrastructures, platforms, and software applications as services to users on the basis of a usage-based pricing model. As Cloud-based systems have been increasing in size and complexity and operate in a continuously and unpredictably changing environment, it has become increasingly more important and challenging to develop effective provisioning and pricing schemes. In this paper we consider several Software as a Service (SaaS) providers, that offer a set of Web services using the Cloud facilities provided by an Infrastructure as a Service (IaaS) provider. We assume that the IaaS provider offers a pay only what you use scheme similar to the Amazon EC2 service, comprising flat, on demand, and spot virtual machine instances. We propose a two stage provisioning scheme. In the first stage, the SaaS providers determine the number of required flat and on demand instances by means of standard optimization techniques. In the second stage the SaaS providers compete, by bidding for the spot instances which are instantiated using the unused IaaS capacity. We assume that the SaaS providers want to maximize a suitable utility function which accounts for both the QoS delivered to their users and the associated cost. The IaaS provider, on the other hand, wants to maximize his revenue by determining the spot prices given the SaaS bids. We model the second stage as a Stackelberg game, and we compute its equilibrium price and allocation strategy by solving a Mathematical Program with Equilibrium Constraints (MPEC) problem. Through numerical evaluation we study the equilibrium solutions as function of the system parameters.