Quality of information (QoI) provides a context-dependent measure of the utility that a network delivers to its users by incorporating non-traditional information attributes. Quickly and easily predicting performance and limitations of a network using QoI metrics is a valuable tool for network design. Even more useful is an understanding of how network components like topology, bandwidth, and protocols, impact these limitations. In this paper, we develop a QoI-based framework that can provide accurate estimates for limitations on network size and achievable QoI requirements, focusing on completeness and timeliness. We extend this framework to model competing flows and data loads as random variables to capture the stochastic nature of real networks. We show that our framework can provide a characterization of delays for satisfied queries to further analyze performance when some late arrivals are acceptable. Analysis shows that the large tradeoffs exist between network parameters, such as QoI requirements, topology, and network size. Simulation results also provide evidence that the developed framework can estimate network limits and delays with high accuracy. Finally, this paper also introduces scalably feasible QoI regions, which provide upper bounds on QoI requirements that can be supported for certain network applications.