||A problem encountered in the analysis of telecommunication systems, as well as in other distribution systems, is that of estimating the performance level of the system in meeting user demands with available resources. In particular, the user demands and the available resources are only assumed to be known stochastically, and communication links may operate at various levels. This situation can be modeled as a stochastic network flow problem, in which each edge of the network assumes a finite number of values (corresponding to different capacity levels) with known probabilities. In each state of the network, there are deterministic supplies, demands, and link capacities, and we are interested in whether overall demand can be met using the present supply of resources. If not, we are interested in the maximum demand that can be met using the best allocation of flows. The approach used here to estimate the probability of unmet demand, as well as the average unmet demand, involves generating only "high leverage" states of the system──states having high probability and/or high values of unmet demand. A new method is proposed for generating such states and producing bounds on various performance measures for the system.