In the 303x input/output system certain jobs are critical in the sense that the system pays a penalty in reduced performance if they are not finished in some maximum allowable time. The purpose of the model is to determine the extent of the penalty a system will pay in a heavily loaded environment. The model of the input/output system of the 303x processors decomposes the system into a three level hierarchy of server/requestors. The levels are: 1. (highest) the teleprocessing controllers, 2. the byte channel interface, and 3. (lowest) the director of the 303x channel group. In a typically heavily loaded situation, the rare situations when the queues for the shared resources become excessive, some jobs may pay a performance penalty. The analytic techniques used to determine the probability of these rare situations of excessive queue length and the model validation results will be described.