This paper presents resource management techniques for allocating communication and computational resources in a distributed stream processing platform. The platform is designed to exploit the synergy of two classes of network connections -- dedicated and opportunistic. Previous studies we conducted have demonstrated the benefits of such bi-modal resource organization that combines small pools of dedicated computers with a very large pool of opportunistic computing capacities of idle computers to serve high throughput computing applications. This paper extends the idea of bi-modal resource organization into the management of communication resources. Since distributed stream processing applications demand large volume of data transmission between processing sites at a consistent rate, adequate control over the network resources is important to assure a steady flow of processing. The system model used in this paper is a platform where stream processing servers at distributed sites are interconnected with a combination of dedicated and opportunistic communication links. Two pertinent resource allocation problems are analyzed in details and solved using decentralized algorithms. One is the mapping of the stream processing tasks on the processing and the communication resources. The other is the adaptive re-allocation of the opportunistic communication links due to the variations in their capacities. Overall optimization goal is higher task throughput and better utilization of the expensive dedicated links. The evaluation demonstrates that the algorithms are able to exploit the synergy of bi-modal communication links towards achieving the optimization goals.