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In the service oriented paradigm applications are created as a composition of independently developed Web services. Since the same service may be offered by different providers with different non-functional Quality of Service (QoS) attributes, a selection process is needed to identify the constituent services for a given composite service that best meet the users QoS requirements. In this paper, we consider a broker that offers a composite service with multiple QoS classes to several users each generating a flow of requests over time. We propose a service selection scheme which optimizes the end-to-end aggregated QoS of all incoming flows of requests by means of a simple linear programming problem which scales as the number of users, request volumes and/or services grows. This approach differs from most of the current proposals which may not scale well since: a) requests, even from the same user, are handled independently from one another; and b) the selection process often requires the solution of an NP-hard problem.