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This paper presents a case for exploiting the synergy of dedicated and opportunistic network resources in a distributed hosting platform for data stream processing applications. Our previous studies have demonstrated the benefits of combining dedicated reliable resources with opportunistic resources in case of high-throughput computing applications, where timely allocation of the processing units is the primary concern. Since distributed stream processing applications demand large volume of data transmission between the processing sites at a consistent rate, adequate control over the network resources is important here to assure a steady flow of processing. In this paper, we propose a system model for the hybrid hosting platform where stream processing servers installed at distributed sites are interconnected with a combination of dedicated links and public Internet. Decentralized algorithms have been developed for allocation of the two classes of network resources among the competing tasks with an objective towards higher task throughput and better utilization of expensive dedicated resources. Results from extensive simulation study show that with proper management, systems exploiting the synergy of dedicated and opportunistic resources yield considerably higher task throughput and thus, higher return on investment over the systems solely using expensive dedicated resources.