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In this work a family of tension trigonometric curves analogous to those of cubic Bézier curves is presented. Some properties of the proposed curves are discussed. We propose an efficient interpolating method based on the tension trigonometric splines with various properties, such as partition of unity, geometric invariance and convex hull property, etc. This new interpolating method is applied to construct curves and surfaces. Moreover, one can adjust the shape of the constructed curves and surfaces locally by changing the tension parameter, the latter is included mainly because of its importance for object visualization. To illustrate the performance and the practical value of this model as well as its accuracy and efficiency, we present some modeling examples.Mathematics Subject Classification: 65T40, 65D05, 65D17, 76B45.

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In the last decades cloud computing has been the focus of a lot of research in both academic and industrial fields, however, implementation-related issues have been developed and have received more attention than performance analysis which is an important aspect of cloud computing and it is of crucial interest for both cloud providers and cloud users. Successful development of cloud computing paradigm necessitates accurate performance evaluation of cloud data centers. Because of the nature of cloud centers and the diversity of user requests, an exact modeling of cloud centers is not practicable; in this work we report an approximate analytical model based on an approximate Markov chain model for performance evaluation of a cloud computing center. Due to the nature of the cloud environment, we considered, based on queuing theory, a MMPP task arrivals, a general service time for requests as well as large number of physical servers and a finite capacity. This makes our model more flexible in terms of scalability and diversity of service time. We used this model in order to evaluate the performance analysis of cloud server farms and we solved it to obtain accurate estimation of the complete probability distribution of the request response time and other important performance indicators such as: the Mean number of Tasks in the System, the distribution of Waiting Time, the Probability of Immediate Service, the Blocking Probability and Buffer Size…

In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using the derivatives are presented. The combination of tension, continuity, and bias control is used as a very powerful type of interpolation; they are applied to open and closed Hermite interpolation curves. Surface construction utilizing the studied trigonometric Hermite interpolation is explored and several examples obtained by the C1 trigonometric Hermite interpolation surface are given to show the usefulness of this method.