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We advocate the notion of service overlay network (SON) as an effective means to address some of the issues, in particular, end-to-end quality of service (QoS), plaguing the current Internet, and to facilitate the creation and deployment of value-added Internet services such as VoIP, Video-on-Demand, and other emerging QoS-sensitive services. The SON purchases bandwidth with certain QoS guarantees from the individual network domains via bilateral service level agreement (SLA) to build a logical end-to-end service delivery infrastructure on top of the existing data transport networks. Via a service contract, users directly pay the SON for using the value-added services provided by the SON. In this paper, we study the bandwidth provisioning problem for a SON which buys bandwidth from the underlying network domains to provide end-to-end value-added QoS sensitive services such as VoIP and Video-on-Demand. A key problem in the SON deployment is the problem of bandwidth provisioning, which is critical to cost recovery in deploying and operating the value-added services over the SON. The paper is devoted to the study of this problem. We formulate the bandwidth provisioning problem mathematically, taking various factors such as SLA, service QoS, traffic demand distributions, and bandwidth costs. Analytical models and approximate solutions are developed for both static and dynamic bandwidth provisioning. Numerical studies are also performed to illustrate the properties of the proposed solutions and demonstrate the effect of traffic demand distributions and bandwidth costs on SON bandwidth provisioning.