Analytic solutions are sought for various special cases of a general scheduling model based on the following assumptions: 1) work is scheduled on a single processor, 2) the scheduling objective is to maximize service rendered, 3) a loss function associated with each request reflects the decline in utility caused by its delayed completion, 4) each request is associated with a request class for which the distribution of service times is know, 5) the process by which new requests arrive is known for each request class, and 6) preemption of a request not yet completed requires a fixed amount of processor time. After a detailed examination of the model and a discussion of past work on related models, various special cases are studied.