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This paper examines congestion control issues for TCP flows that require in-network processing on the fly in network elements such as gateways, proxies, firewalls and even routers. Applications of these flows are increasingly abundant in the future as the Internet evolves. Since these flows require use of CPUs in network elements, both bandwidth and CPU resources can be a bottleneck and thus congestion control must deal with "congestion" on both of these resources. In this paper, we show that conventional TCP/AQM schemes can significantly lose throughput and suffer harmful unfairness in this environment, particularly when CPU cycles become more scarce (which is likely the trend given the recent explosive growth rate of bandwidth). As a solution to this problem, we establish a notion of dual-resource proportional fairness and propose an AQM scheme, called Dual-Resource Queue (DRQ), that can closely approximate proportional fairness for TCP Reno sources with in-network processing requirements. DRQ is scalable because it does not maintain per-flow states while minimizing communication among different resource queues, and is also incrementally deployable because of no required change in TCP stacks. The simulation study shows that DRQ approximates proportional fairness without much implementation cost and even an incremental deployment of DRQ at the edge of the Internet improves the fairness and throughput of these TCP flows. Our work is at its early stage and might lead to an interesting development in congestion control research.