As part of a project designed to construct a mathematical model of the operation of an academic library, a research team determined the usefulness of a quantitative approach to making decisions about the number of copies of each item that a university library should provide. Using the reserve collection of the University of Lancaster Library as a basis, a mathematical relationship was established between the number of requests, the length of the loan period, the number of copies, and a standard of service (defined as "immediate availability"). It was found that the Poisson distribution could justifiably be used to relate the average request rate to the number of copies and the degree of availability likely to be achieved. A table was produced which can be used in a predictive manner insofar as the request rate itself can be predicted. A method of estimating the average request rate from incomplete data was also devised. It was concluded that a mathematical relationship between the factors concerned can be established. The chief difficulty lies in predicting the level of demand for library services and, more generally, in understanding the factors which determine it. (JB)