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The Grid is an integrated infrastructure that can play the dual roles of a coordinated resource consumer as well as a donator in distributed computing environments. In a mobile grid environment, the Grid acts as a resource hungry consumer whereas in ubiquitous computing environments, it has the inherent potential to provide services to applications. The enormous growth in the use of mobile and embedded devices in ubiquitous computing environment and their interaction with human beings produces a huge amount of data that needs to be processed swiftly anytime anywhere. However, most devices used in ubiquitous environments have limited resources in terms of CPU, storage, battery power and communication bandwidth. In such ubiquitous computing platforms, there is a need to transfer application services to computational resources. In this paper, we investigate the use of the Grid as a candidate for provisioning computational services to applications in ubiquitous computing environments. In particular, we present a competitive model that describes the possible interaction between the competing resources in the Grid Infrastructure as service providers and ubiquitous applications as subscribers. The competition takes place in terms of quality of service (QoS) offered by different Grid Service Providers. The ubiquitous users' resource demands depend not only on the QoS parameters (e.g., response time and loss probability in our context) offered by that service provider but also upon those of its competitors. We develop a stochastic equilibrium model for QoS assurance. Based upon those QoS parameters, we propose two types of demand models whose distribution functions are closely correlated with service level QoS parameters. We proceed to present the equilibrium behavior of our model facing global competition under stochastic demand and estimation of guaranteed QoS assurance level satisfying the requirement of ubiquitous application efficiently. Simulation results show that our proposed framework maximizes the provider's expected revenue at the optimal point of different QoS parameters.