Abstract We propose a stylized model of a problem-solving organization whose internal communication structure is given by a fixed network. Problems arrive randomly anywhere in this network and must find their way to their respective specialized solvers by relying on local information alone. The organization handles multiple problems simultaneously. For this reason, the process may be subject to congestion. We provide a characterization of the threshold of collapse of the network and of the stock of floating problems (or average delay) that prevails below that threshold. We build upon this characterization to address a design problem: the determination of what kind of network architecture optimizes performance for any given problem arrival rate. We conclude that, for low arrival rates, the optimal network is very polarized (i.e. star-like or centralized), whereas it is largely homogenous (or decentralized) for high arrival rates. These observations are in line with a common transformation experienced by information-intensive organizations as their work flow has risen in recent years.