Feedback is used in many network algorithms and networked applications. Yet, in most cases, feedback is not received immediately; instead, feedback delay is very common due to the nature of network communication. In the worst-case, the network can be congested, resulting in a huge feedback delay, which is likely to bring negative impacts to the provided service. In this thesis, we mainly focus on a dual-path Network Utility Maximization (NUM) framework, which targets the optimization of resource allocation for image crowd-processing. As part of this system, an estimate of hit rate is used to allocate resources. We consider the impact of feedback delay on predicting hit rate, which can be a threat to the NUM performance.