In this paper, we consider a shared data center (or web server) with requests from multiple companies: each company with two classes of request: 1) streaming requests and 2) elastic requests. The processing capacity of the web server is shared by the companies' requests of the two classes. An analytical model is developed and matrix geometric method is used to derive the system performance measures. A cost model is developed to obtain a request admission control policy that utilizes the web server's processing capacity efficiently. The objective is to maximize the revenue of the data center, which is a function of the multiclass request characteristics and the quality of service measures. It is well known that the request characteristics like arrival rates vary dynamically over time. As a consequence, autonomic computing is the only practical way for determining on the fly how to partition the web server processing capacity over time among the companies.