Optimal Pricing and Service Provisioning Strategies in Cloud Systems: A Stackelberg Game Approach

Abstract

Abstract-In this paper we consider several Software as a Service (SaaS) providers, that offer a set of applications 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.

Bidding Strategies in QoS-Aware Cloud Systems Based on N-Armed Bandit Problems

“…Modeling the cost as a linear function of the response time is an approximation: a fixed penalty whenever the maximum response time is exceeded would be more realistic; in addition, usually revenue does not scale linearly since stocks may give rise to discounts. Nevertheless, this allows us: (1) to consider a soft constraint on the response time, which enables the SaaS provider to trade-off revenues and infrastructural costs [20], [21]; (2) to model the SaaS providers gain to let them buy more VMs than the bare essential in order to satisfy the SLA, to increase the application reliability and performance and, in turn, their reputation.…”

“…Under the assumption of perfect load sharing among multiple VMs assigned to the same application, we have the following general expression for the per-hour SaaS profit (see [20], [21]); the first term represents the SaaS provider revenue, while the others the cost to use the IaaS provider facilities:…”

“…In this paper we follow the approach proposed in [21] and we consider a two-stage allocation procedure. In the first one, each SaaS provider independently determines, for each offered service, the number of flat and on demand instances 1 which guarantees the performance level defined in the SLA to his prospective users and maximizes his profit.…”

“…Constraint (5) guarantees that resources are not saturated, in particular that their utilization is less than a threshold U max u . Note that, as in [20], [21], we deal with a relaxation of the real problem, because we do not impose to the variables to be integers. Otherwise, the problem would be too difficult to solve (i.e., NP-hard).…”

“…We assume that the IaaS provider has always enough resources to accomodate the SaaS providers demand. For each SaaS provider u ∈ U we have the following optimization problem, as explained in [21]:…”