The development of a mathematical model of the Illinois Library and Information Network (ILLINET) is described. Based on queueing network theory, the model predicts the probability of a request being satisfied, the average time from the initiation of a request to the receipt of the desired resources, the costs, and the processing loads. Using a hypothetical network, two sets of operating policies are analyzed: those emphasizing minimum delay and those that maximize the probability of successfully meeting user requests. Cost constraints and value judgements about tradeoffs between delays and the probability of satisfying user requests are considered in the context of network operating policies. The impact of union listings of holdings, automated circulation at the individual libraries, and computer-controlled networks is analyzed. Future plans for network modeling together with the equations used in the network simulation are also presented. (DGC)