In this project, the investigator is studying an approach to mathematically simulating the relationships between assimilative capacities that flowing streams have for pollutants and the pollutants that are derived from both point and non-point sources. Whereas past efforts to do this have assumed that stream-flow was the sole random variable, in this research, the investigator is considering as random variables the initial in- stream conditions regarding oxygen demand and oxygen resources, pollutant input demand on those resources, and the various mathematical-model coefficients that have previously been assumed to be constants.