We consider a three-tier architecture for mobile and pervasive computing scenarios, consisting of a local tier ofmobile nodes, a middle tier (cloudlets) of nearby\ud computing nodes, typically located at the mobile nodes access points but characterized by a limited amount of resources, and a remote tier of distant cloud servers, which have practically infinite resources. This architecture has been proposed to get the benefits of computation offloading from mobile nodes to external servers while limiting the use of distant servers whose higher latency could negatively impact the user experience.\ud For this architecture, we consider a usage scenario where no central authority exists and multiple non-cooperative mobile users share the limited computing resources of a close-by cloudlet and can selfishly decide to send their computations to any of the three tiers. We define a model to capture the users interaction and to investigate the effects of computation offloading on the users’ perceived performance. We formulate the problem as a generalized Nash equilibrium problem and show existence of an equilibrium.We present a distributed algorithm for the computation of an equilibrium which is tailored to the problem structure and is based on an in-depth analysis of the underlying equilibrium problem. Through numerical examples, we illustrate its behavior and the characteristics of the achieved equilibria

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.

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